What substitutes for prayers for the Pope's intentions during sede vacante?

I made some research myself, and I found that someone tried hard to learn after death of John Paul II. Here is an English translation of a latin answer from the office of Apostolic Penitentiary, answering our question:

Most eminent father;

Geoffrey W. Horton of the Seminary of the of Baltimore Archdiocese under the title of Mount St. Mary's in the city of Emmittsburg, in a letter dated the 4th of April 2005, puts forth the following questions:

1. In regards to the prayer prescribed for the intention of the Supreme Pontiff for gaining a plenary indulgence (cf. "The Manual of Indulgences", 4th edition, Norm. 2. 20 paragraph 1), if in the vacancy of the Apostolic see the faithful are impeded in procuring said plenary indulgence. And to what point they are not be impeded.
2. How in this condition, with the Apostolic See vacant, the plenary indulgence is fulfilled. And God, etc.

April 13th, 2005

The Apostolic Penitentiary responds to the proposed question:

To the first question: No, the faithful can seek a plenary indulgence even in the time of a vacant Apostolic See. To the second question:
Even though the Apostolic See is vacant, the conditions of praying for the intention of the Supreme Pontiff are fulfilled (by reciting once the "Our Father" and the "Hail Mary" once; nevertheless, the opportunity is also given to the individual faithful to recite another prayer which pleases them according to the piety and devotion of each one), even if he has fulfilled the duty of his life, since the ends of the Pope's intention, the ends for which one must pray--undoubtedly the spiritual good of the whole Church -- persist.

John Francis Girotti, OFM Conv.

John Mary Gervais

The answer is awesome: Communion of Saints! It's the pope's job to pray for the Church (and while we pray for the intention of the Sovereign Pontiff, we support mainly this kind of prayers). If he does it while living as a member of ecclesia militans, he will certainly continue in heaven or purgatory.
There is a problem when a pope doesn't pray for the Church, either because he lives and is prayer-lazy or because he is dead and damned, but I don't think either will be the case of Joseph Ratzinger in March.

Each year, the Vatican announces the Pope's Intentions for the year ahead (see e.g. http://www.ewtn.com/faith/papalprayer.htm ) - so by praying for the intentions the last Supreme Pontiff indicated for that month, surely you are praying for the Pope's Intentions, even when there is no current Pope?

It's not a prayer for the Pope; it's a prayer for the intention of the Pope.

From the Enchiridion of Indulgences issued on 29 June 1968:

26. To acquire a plenary indulgence it is necessary to perform the work to which the indulgence is attached and to fulfill the following three conditions:

• sacramental confession,
• Eucharistic Communion,
• and prayer for the intention of the Sovereign Pontiff.

It is further required that all attachment to sin, even venial sin, be absent.

If the latter disposition is in any way less than perfect or if the prescribed three conditions are not fulfilled, the indulgence will be partial only.

29. The condition of praying for the intention of the Sovereign Pontiff is fully satisfied by reciting one Our Father and one Hail Mary; nevertheless, each one is free to recite any other prayer according to his piety and devotion.

Although certain functions of the Papacy are carried out during a vacancy under the Cardinal Camerlengo, there is no "Sovereign Pontiff".

Given that a prayer for the intention of the Sovereign Pontiff cannot be properly fulfilled in a vacancy, it would appear that any indulgence will be partial only.