Quote Originally Posted by Martok
To be honest, I'm not really sure what determines which factions the Pope gives money, nor why he does it. About the only thing we know with any certainty is that he apparently only gives money to Catholic factions that can Crusade. So if you play as the Danes, Polish, or Hungarians, you won't get any money from him.

Aside from that, however, the question is something of a mystery.
Well, pious kings tend to get more money from the Pope - that and kingdoms who wage wars against Muslims/Pagans. I almost always recieve a gift from the Pope shortly after invading a non-Christian province. Sometimes just being pious and leaving your Catholic brethren alone seems to be enough though, as both the HRE and the English usually receive a lot of money in Early, and none of these factions have an opportunity to fight pagans right away.