What I want to see is more incentive to be friendly with other civilization, rather than just disincentive to be hated by them. Basically, I think the current system focuses too much on punishing you for having bad relationships with other civilizations, rather than rewarding you for having good relationships with them. The only reasons I see to be friendly with them is to not be invaded by them and for them to be a little more reasonable when making trades (rather than refusing trades that are favorable to them just because they hate you). And when there's so much you can to do anger them, like expanding too much, doing any kind of conquest, or allying city states they wanted to ally, it's much harder to win the game without doing any of those, than it is to win the game by just being a douche to everyone and not caring what they think about you.
An example of a good improvement would be trade routes with AI civs. Obviously you would have to be really friendly with them for this to work, but there would actually be incentive to try getting friendly with other civs, and hopefully some incentive for them to not just suddenly decide to invade you.
I can't be the only one who finds it ridiculous that when they hate you, they'll be completely ridiculous and do stuff like demand all your luxury resources for one of theirs, when they could have actually have made a really good trade by accepting two of your luxury resources for one of theirs. But when you are really friendly with them and have done lots of good stuff for them, the best kind of trade you can get with them is still one that is equally beneficial to both parts, they never agree on taking the short end of the stick. So after all that effort you put into maintaining good relationships with other civs, all you get out of it is that they tolerate you. At least for me, that's not a very inspiring goal to strive for at all.