In my recent Epeiros campaign I had a pretty good diplomatic situation. I had the Getai, Pontos and once I conquered Italy the Aedui as neighbors.

I tributed each faction 500 mnai\turn and asked them to a attack a faction they were at war with. I played until 218 BC (CTD) and only had problems with the Getai. After winning the war in about 230 BC I made them my loyal protectorate for the rest of the game. The Aedui were even more loyal since my money was the only thing saving the from the Sweboz, Arveni and the Lusitannans.

From what I can understand from this it is better to tribute (I tributed for 50 and later 100 turns) rather than do single payments and to ask the other factions to attack another faction in exchange for that tribute. And having large garrisons in the all border settlements also helps keep the peace.

I was also using FD but kept my proposals realistic.