Using a PoD after AD 100 (for the sake of picking a date) posit a way the Papacy could evolve into the office of Caliph, that is: a dynasty rule merged with faith leader for in theory, the entire Christian world. I know that this was basically the Byzantine Emperor in the east, but from the beginning it was Pope and Emperor or Patriarch and Emperor. So I'm thinking Emperor as Pope in a way that is like the Caliphate, where even when Baghdad was conquered the various dynasties still acknowledged him as Caliph, he was just a puppet for a while.
While I can't think of a specific POD, I would say you need to cancel out the reforms(Gregorian, I think?) of the middle ages. If the secular and the sacred are more intertwined, there's more potential for an Emperor to take the position.
I would put forward that, if people get used to the idea of the sacred and secular as one in the same you might get the possibility of one being the other. I'd also say have one very large empire covering Europe, so that the Papacy is dependant on only one state and can't play several off of each other. From there, maybe have either a succession of Popes or Emperors that makes a period of greatness/peace fall apart or a huge heretical tyrant. Civil War between the Papacy-backers and Imperial-backers ensues, and the winner claims the other's title to "protect it from future abuse". Remove the doctrine that priests can't be married, and voila, possible hereditary leader.
Not sure if that would really help, considering it takes a lot of changes and more than a little more fantastic things, but that's all I got.