I never really figured this out, and the various ideas behind it I read on these forums seemed mixed. However, the times I've received the most papal cash was when I played Poland, Hungary or Sicily. I don't think I ever received papal cash when playing France, England, Italy. So who knows.

A couple times the Pope handed me cash when they were getting pasted by the Italians. You would have thought they could have used the cash themselves to fight them off.