Authentic Supplication Number 158.

'Abi 'Umamatah said that a companion of the Prophet  told him: The sunnah with respect to the funeral prayer is that the Imam pronounce the takbeerah (174), then, that he silently read the opening surah of the Qur'an after the first pronunciation of the takbeerah. Then, that he petition salat (175) upon the Prophet , and that he make sincere supplication for the corpse over the following (three) takbeeras, not reciting [Qur'an] in any of them. Then he should make tasleem silently in himself (when he steps out of the prayer ([turning] to his right), and the sunnah is that those behind him do as their Imam did) (176).

Footnotes.
(174) This is to say 'Allahu 'akbaru.
(175) Ask Allah to bestow honor, and grace upon the Prophet . Al-'Albani said that he had not come across any specific funeral-related wording for petitioning salat upon the Prophet , saying that any of the authentic wordings used in tashahhud would be correct.
(176) Al-'Albani said that the wording: "Then, that he petition salat upon the Prophet , and that he make sincere supplication for the corpse over the following (three) takbeeras" indicates that the petitioning of salat upon the Prophet  is done after the second takbeerah, not before that, because if it were before it would not fall into the (three) takbeeras, it would fall before that. The parentheses are related to the references for this hadeeth in the hadeeth reporters section.

Reporters.
Al-'Albani said, in his 'Ahkam 'Al-Jana'iz wa Bida`iha that it was reported by Al-Shafi`iy in his Al-'Um, 239-240/1. He said that the squiggly brackets were reported by Al-Hakim, 360/1; and that Al-Hakim said it was sound according to the conditions of Al-Bukhari, and Muslim; that Ath-thahabi agreed; and that so did he.