I had terrible relations with Pope, i was excommunicated and after finishing Sicilians i wanted to reconciliate with Pope. I couldnt get it in one go so i started slowly. I gave him a gift 800 florints tribute for 5 turns i think.
Every turn my relationship was better and better. After 3 or 4 turns i asked again for lifting excommunication. He still was a bit pissed of but at least he now was willing to do it for 3 turn tribute of 6666. Fortunately i pass the ofer and he died in the next turn. New Pope lifted excommunication and i gave him a gift of 1500 for it. Now he loves me. I have second best standing with him. He even started to promote my priests (never happened before).
Other situation was when i had to cross my ally territory with family character. I wanted to get right of passage but they didnt agree. So i just walked through they land. They where a bit pissed of about it so i just payed them 800 florints of damages and our relationships where back to the level before incident.