Is the supplication authentically reported from the Prophet, peace and blessings be upon him, regarding the funeral prayer obligatory, or is it permissible to use other supplications?

The purpose of the funeral prayer (Salat al-Janazah) is to supplicate for the deceased. Supplications have been reported from the Prophet (peace and blessings be upon him), among them: "O Allah, forgive him, have mercy on him, grant him well-being, and pardon him..." and "O Allah, forgive our living and our dead...". It is preferable to supplicate with these reported supplications, but there is no harm in supplicating with others, for the Prophet (peace and blessings be upon him) said: "When you pray over the deceased, then be sincere in supplicating for him." So, the important thing is sincerity in supplicating for the deceased, in any form.