Even if you do give them gifts, that'll just change their attitude to annoyed. They still will refuse to trade with you, no matter how large the gifts, or how often they recieve them. Should you manage to get them to polite or gracious (most likely through MPPs/alliances) they still will not be any more willing to deal with you.
The AI moods really don't stand for anything. A polite civ will backstab you, a furious one will send thousands of troops to die for your cause, giving back every conquered city will still leave their owner furious with you for the rest of the game.
It would be nice if we could have some sort of screen that keeps track of treaties, its tedious to enter diplomacy and check the active trades screen for each individual civ. Maybe they could just present us with a popup, "Doing this will break treaty x with the [civ], Do you wish to continue?
One mistake in 750 BC can ruin the entire game, as nobody will forgive, or forget.