Sometimes the Popes will give you missions and that helps immensely. I'm not sure if having good Papal relations has anything to do with diplomacy with the Papal States, but you can try that.

Originally posted by RuskieBusiness:

Sometimes the Popes will give you missions and that helps immensely. I'm not sure if having good Papal relations has anything to do with diplomacy with the Papal States, but you can try that.

I will give it a try, thanks for the advice!

It seems that giving the Pope money doesn't really do anything beyond help your standing with the faction, itself, but not the Pope, personally. But it also seems that you can increase your standing with the Pope by showing mercy to defeated Catholic armies. Instead of executing enemy captives after a battle, ransoming and releasing them seems to have helped me gain more favour with the Pope. Executing captured Catholic soldiers has the opposite effect and will hurt your standing with the Pope. This even seems to be the case when fighting rebellions and civil wars; the Pope still prefers you show mercy to other Catholics. As far as I can tell, looting enemy Catholic settlements seems to be tolerated by the Pope, though.
I haven't played enough yet to see how the Pope feels about you murdering Cathars, but if he's anything like actual 13th century popes then he either likely won't care or might even reward you.

How do you accept the pope's quests and or his crusades they keep popping up an I can do anything