What is the earliest-known list of the Roman Principate?

Short Answer:

I don't know when the first mere list of Roman Emperors that included the entire Principate period of 27 BC to AD 284 was written, but the oldest surviving such list was probably written several centuries after AD 284 and thus it probably included a number of western and/or eastern Roman emperors up to the date when it was written.

Long Answer:

It is very difficult to make an accurate list of Roman emperors (which makes such list making interesting) even for such a short period of the Roman Empire as the 311 years of the Principate.

In order to make a consistent list of Roman Emperors, someone needs to have a set of criteria to determine who was an emperor and who wasn't one and to apply those criteria consistently. Since it is possible to disagree about the various criteria necessary to certify someone as an emperor, it is possible for different people to produce different lists of Emperors.

Wikipedia has a list of Roman Emperors, https://en.wikipedia.org/wiki/List_of_Roman_emperors1

And a list of Roman Usurpers, who claimed to be emperor but are not recognized as emperors: https://en.wikipedia.org/wiki/List_of_Roman_usurpers2

The Wikipedia list of Roman emperors acknowledges that separating Emperors from usurpers is difficult and subjective, and list three criteria for inclusion as "legitimate" emperors:

Any individual who undisputedly ruled the whole Empire, at some point, is a 'legitimate emperor'(1).

Any individual who was nominated as heir or co-emperor by a legitimate emperor (1), and who succeeded to rule in his own right, is a legitimate emperor (2).

Where there were multiple claimants, and none were legitimate heirs, the claimant accepted by the Roman Senate as emperor is the legitimate emperor (3), at least during the Principate.

https://en.wikipedia.org/wiki/List_of_Roman_emperors#Legitimacy3

Ancient Romans used the consular dating, naming the years after the two consuls for the year, as their most common method of dating. So naturally they needed lists of the years and the two consuls for each year.

Fasti consulares were official chronicles in which years were denoted by the respective consuls and other magistrates, often with the principal events that happened during their consulates, but sometimes not.

https://en.wikipedia.org/wiki/Fasti

So the Roman habit of making lists of consuls would naturally suggest making lists of Roman emperors, and no doubt many different Romans made lists of emperors at various times.

The Historia Brittonum was written about AD 830. The writer sometimes dates events by consular dating. Thus there were lists of Roman consuls even in remote Wales during the Dark Ages.

It has a list of nine Roman Emperors who traveled to Britain. Sections 19 to 27 list the emperors from Julius Caesar, who is not usually considered an emperor, to a Constantinus who allegedly reigned 16 years in Britain.

The list includes both Claudius and Severus, who were definitely emperors ruling during the Principate period of 27 BC to AD 284.

See my answer here: https://www.quora.com/Which-Roman-emperors-set-foot-in-Britain4

The oldest collection of Welsh genealogies is the Harleian Genealogies.

The Harleian genealogies are a collection of Old Welsh genealogies preserved in British Library, Harley MS 3859. Part of the Harleian Library, the manuscript, which also contains the Annales Cambriae (Recension A) and a version of the Historia Brittonum, has been dated to c. 1100, although a date of c.1200 is also possible.1 Since the genealogies begin with the paternal and maternal pedigrees of Owain ap Hywel Dda (d. 988), the material was probably compiled during his reign.1 The collection also traces the lineages of less prominent rulers of Wales and the Hen Ogledd. Some of the genealogies reappear in the genealogies from Jesus College MS 20.

https://en.wikipedia.org/wiki/Harleian_genealogies5

One of the pedigrees apparently includes most of the Roman Emperors of the Principate period and some of the Dominate period.

It is believed that someone took a list of Roman Emperors in chronological order, and copied it in reverse chronological order, putting "ap", meaning "son of", between each name to convert a list of rulers into a pedigree. As I remember, the pedigree has most of the emperors of the Principate listed in chronological order.

So even in remote Wales during the Dark Ages, written lists of Roman Emperors in chronological order were available.

A number of Roman historians wrote histories of the imperial period, and of course they mentioned when emperors died and new emperors took power. So anyone who had access to such a text, could copy out from it a list of Roman Emperors for he period that it covered.

Gaius Suetonius Tranquillus wrote the famous Lives of the Twelve Caesars about AD 121, giving biographies of Gaius Julius Caesar and the first 11 Roman Emperors. Thus Suetonius more or less made a list of persons he considered to be "Caesars" and/or Roman Emperors. Any persons who might be considered emperors by some persons but don't have separate biographies in the book would people that Suetonius didn't count as Roman Emperors.

For example, Augustus, the first Emperor, selected several persons to be his heirs, but they all died before Augustus, except for the last, Tiberius. Some people might consider them to Emperors of a sort, since they were granted some or all of the honors and powers of Augustus, but Suetonius did not.

https://en.wikipedia.org/wiki/The_Twelve_Caesars6

The Historia Augusta (English: Augustan History) is a late Roman collection of biographies, written in Latin, of the Roman Emperors, their junior colleagues, designated heirs and usurpers of the period 117 to 284. Supposedly modeled on the similar work of Suetonius, The Twelve Caesars, it presents itself as a compilation of works by six different authors (collectively known as the Scriptores Historiae Augustae), written during the reigns of Diocletian and Constantine I and addressed to those emperors or other important personages in Rome. The collection, as extant, comprises thirty biographies, most of which contain the life of a single emperor, while some include a group of two or more, grouped together merely because these emperors were either similar or contemporaneous.1

The true authorship of the work, its actual date, its reliability, and its purpose, have long been matters for controversy amongst historians and scholars, ever since Hermann Dessau in 1889 rejected both the date and the authorship as stated within the manuscript. Major problems include the nature of the sources it used, and how much of the content is pure fiction. For instance, the collection contains in all about 150 alleged documents, including 68 letters, 60 speeches and proposals to the people or the senate, and 20 senatorial decrees and acclamations. Virtually all of these are now considered to be fraudulent.2

By the second decade of the 21st century, the overall consensus supported the position that there was only a single author who was writing either at the end of the 4th century or the beginning of the 5th century, and who was interested in blending contemporary issues (political, religious and social) into the lives of the 3rd century emperors. There is further consensus that the author used the fictitious elements in the work to highlight references to other published works, such as to Cicero and Ammianus Marcellinus in a complex allegorical game. Despite these conundrums, it is the only continuous account in Latin for much of its period and is thus continually being re-evaluated, since modern historians are unwilling to abandon it as a unique source of possible information, despite its obvious untrustworthiness on many levels.3

https://en.wikipedia.org/wiki/Historia_Augusta7

So the Historia Augusta may be considered a sort of sequel to the Lives of the Twelve Caesars, though there is a gap, the reigns of Nerva and Trajan from AD 96 to 117, which is not covered by either work.

The Enmannsche Kaisergeschichte, in English often called Enmann's Kaisergeschichte (Kaisergeschichte: History of the Emperors), is a modern term for a hypothesized Latin historical work, written in the 4th century but now lost.

The German scholar Alexander Enmann made in 1884 a comparison of several late Roman historical works and found many similarities, which could not be explained by a direct literary relationship between the extant works (Eine verlorene Geschichte der roemischen Kaiser und das Buch De viris illustribus urbis Romae). Enmann postulated a theory of a lost historical work, which was the common source for authors including Aurelius Victor, Eutropius, and the author of the Historia Augusta.1 The work is not mentioned by any late Roman historian, but Enmann's analysis is today largely accepted and modified.2 There are some scholars, especially den Boer, who would question its existence, but the majority accept it.3

The Kaisergeschichte was a brief historical work. It had covered the time from emperor Augustus to 337 or 357.3 Besides the three historians mentioned above, it was used by Festus, Jerome, and the anonymous Epitome de Caesaribus.

https://en.wikipedia.org/wiki/Enmannsche_Kaisergeschichte8

Sextus Aurelius Victor (c. 320 – c. 390) was a historian and politician of the Roman Empire.

Aurelius Victor was the author of a short history of imperial Rome, entitled De Caesaribus and covering the period from Augustus to Constantius II. The work was published in 361. Under the emperor Julian (361-363), Victor served as governor of Pannonia Secunda; in 389 he became praefectus urbi (urban prefect), senior imperial official in Rome.1

https://en.wikipedia.org/wiki/Aurelius_Victor9

The Epitome de Caesaribus is a Latin historical work written at the end of the 4th century.

It is a brief account of the reigns of the Roman emperors from Augustus to Theodosius the Great. It is attributed to Aurelius Victor, but was written by an anonymous author who was very likely a pagan. The author used the so-called Enmannsche Kaisergeschichte and the (now lost) Annales of Virius Nicomachus Flavianus (a friend of Quintus Aurelius Symmachus). Although very brief in length and not always reliable, it also contains some useful information.[example needed]

https://en.wikipedia.org/wiki/Epitome_de_Caesaribus10

Flavius Eutropius (fl. around ad 360) was a Roman historian.

His Summary of Roman History (Latin: Breviarium Historiae Romanae) is a ten-chapter compendium of Roman history from its foundation to the accession of Valens. It was compiled with considerable care from the best accessible authorities; it was written in a clear and simple style; and it treats its subjects with general impartiality.3 For the Republican period, Eutropius depended upon an epitome of Livy. For the Empire, he appears to have used Suetonius and the now lost Enmannsche Kaisergeschichte. At the end, he probably made use of his own personal experiences.6

https://en.wikipedia.org/wiki/Eutropius_(historian)11

Festus (fl. 4th century), whose name also appears in the manuscripts of his work as Rufus Festus, Ruffus Festus, Sextus Festus, Sextus Rufus, and Sextus, was a Late Roman historian and proconsul of Asia whose epitome Breviarium rerum gestarum populi Romani ("Summary of the history of Rome"1) was commissioned by the emperor Valens in preparation for his war against Persia. It was completed about AD 370. The Breviarium covers the entire history of the Roman state from the foundation of the City until AD 364. The book consists of 30 chapters treating events in Roman history in terse overview, mainly focused on military and political conflicts. It is estimated as a work of very low quality.2

https://en.wikipedia.org/wiki/Festus_(historian)12

Ammianus Marcellinus (born c. 330, died c. 391 – 400) was a Roman soldier and historian who wrote the penultimate major historical account surviving from antiquity (preceding Procopius). His work, known as the Res Gestae, chronicled in Latin the history of Rome from the accession of the Emperor Nerva in 96 to the death of Valens at the Battle of Adrianople in 378, although only the sections covering the period 353–378 survive.

So if the history of Ammanius Marcellanus survived intact, it would be a complete sequel to Suetonius's Lives of the Twelve Caesars and together they would cover all the emperors from 27 BC to AD 284 as requested, and beyond to AD 378.

Many of the works listed that covered the entire period of 27 BC to AD 284 are much too terse and short for the happiness of historians, but I think that all of them are much too long and informative to count as mere lists of Roman Emperors.

So I don't know when the first mere list of Roman Emperors including the entire Principate period of 27 BC to AD 284 was written, but the oldest surviving such list was probably written several centuries after AD 284 and thus it probably included a number of western and/or eastern Roman emperors up to the date when it was written.