Liturgical prayer in Aramaic?

Presently the Syriac Catholic and Syriac Orthodox churches use Aramaic in their liturgy and chanting

Which Aramaic speaking Christian Church(es) uses a dialect of Aramaic in their liturgy that is the closest to the dialect that Jesus of Nazareth spoke in Palestine some 2000 years ago?

It would seem that the Maronite Catholic Church has the distinction of being the Christian Church that speaks an Aramaic dialect that is the closest dialect of Aramaic that was spoken by Jesus.

The Maronite Liturgy is the original liturgy which developed Antioch in Aramaic right after the time of the Apostles.

Western Neo-Aramaic is a modern Western Aramaic language. Today, it is only spoken in three villages – Maaloula, Bakhah and Jubb'adin – in the Anti-Lebanon Mountains of western Syria. Western Neo-Aramaic is believed to be the closest living language to the language of Jesus, whose first language, according to scholarly consensus, was Western Aramaic; all other remaining Neo-Aramaic languages are of the Eastern branch. It is also spoken by various communities in Lebanon.

Western Neo-Aramaic is probably the last surviving remnant of a Western Middle Aramaic dialect which was spoken throughout the Orontes River Valley area and into the Anti-Lebanon Mountains in the 6th century. It now is spoken solely by the villagers of Maaloula, Jubb'adin and Bakh'a, about 60 kilometres (37 mi) northeast of Damascus. The continuation of this little cluster of Aramaic in a sea of Arabic is partly due to the relative isolation of the villages and their close-knit Christian and Muslim communities. - Western Neo-Aramaic

St. Maron is known as the Father of the Moronite Rite Church. He spoke in Aramaic and was from the region of modern day Lebanon; a time in history that the original Galilean Aramaic was still in full force.

Seeing that St. Maron live in the fourth (4) century A.D. and Aramaic of the Galilean dialect flourished in the region until the sixth (6) century A.D., it makes that the Maronite Church would continue to have the closest dialect of Aramaic that Jesus spoke with his disciples.

Galilean Aramaic (increasingly referred to as Jewish Palestinian Aramaic) is a Western dialect of Aramaic. Its closest contemporary cousins were Samaritan Aramaic and Christian Palestinian Aramaic (CPA), all of which share similar features. While there are a number of modern Eastern Aramaic dialects, the only dialect of Western Aramaic that survives to this day is spoken in the three villages of Ma’loula, Bakh’a, and Jub’addin in Syria (collectively known as the Ma’loula dialect). Sadly with current events and violence in the middle east, the fate of this dialect is uncertain.

Galilean was so very distinct from other contemporary dialects spoken during Jesus’ lifetime, such as Judean Aramaic, that a Galilean could be told apart simply by their speech. Indeed we find this very thing happening in the New Testament:

After a little while the bystanders came up and said to Peter, “Certainly you are also one of them, for your accent betrays you.” – Matthew 26:73

Because of how Galileans spoke differently, early Judean Rabbis thought poorly of them, accusing them of “sloppy speech.” There are several anecdotes in the Talmud Bavli (the “Babylonian Talmud”) where Galileans are mocked due to how they didn’t distinguish between certain consonants and vowels — sounds that were much more distinct and articulate in the prevalent Judean/Babylonian dialect. One such story even forbid Galileans from speaking in the Temple for fear that they might mispronounce something and offend God Himself!

However, despite these differences, after the fall of the Temple in 70 AD, there was a large migration of rabbis from Judea into Galilee, and that is when the dialect flourished. Great works such as Talmud Yerushalemi (the “Palestinian Talmud”) and the Rabba series of Jewish Biblical commentary were penned, and large schools were founded. The era of “Classical” Galilean (the “granddaughter dialect” to that which Jesus spoke) began and it continued into the Byzantine period.

Sadly, in the 600s AD with the rise of the first Patriarchal Caliphate, Galilean was quickly supplanted as the everyday language in Galilee by Arabic, and the linguistically “orphaned” Western, Galilean texts soon fell into the hands of Eastern Aramaic-speaking scribes for preservation.

The following is not meant to be an answer specific to the question, but may help in some research on the subject:

The Syro Malabar and Syro Malankara rites of the Catholic Church in Kerala, India, which attribute their origin to St Thomas the Apostle, used to have their liturgy in Syrian language upto the 1950s after which the liturgy adopted the native language Malayalam as its medium. In fact you will find many short prayers still said in Syrian languae as a part of the liturgy. Besides the Catholic groups, the Catholic Orthodox Churches of Kerala also extensively use Syrian prayers during the liturgical celebrations. How close the phraseology of those prayers are to the dialect used by Jesus, can be commented on by Syrian scholars only.