I agree with you. I don't recall a single time I managed to repair my relationship with a civ back to FRIENDLY status after going to war or having serious issues regarding land or CS politics.
In real life, Europe would be like an ALWAYS-WAR scenario if those limitations in diplomacy were real.
That's because there aren't very many positive modifiers, while there are tons of negative ones. For example, the OP's first mistake was razing a city. Was it the right move if it was in an undesirable location? Probably, but razing a city plus taking over 2 other major ones is quite likely (on Prince) to push you to the #1 civ. If you're #1 in a few categories and relatively weak in military then that just makes other civs even more aggressive towards you. I believe the diplo modifier is "you're trying to win the same way they are". They can covet your lands even if Russia is in between you. They can covet your wonders. You can be competing for the favor of the same CS's. Maybe you were denounced by a friend in the past, etc etc etc.
In the game I finished up yesterday (large, continents, 10 civs/20 city states), I spawned on an isolated continent with only 2 other civs and 4 CS's. I had 20 (TWENTY!!) iron readily available, with 14 of in my capital and city #2. Naturally I killed the other 2 civs. However, while I was mopping them up Liz made contact with me. She hated me for the rest of the game because I was a "warmongering menace". The other civs? 4 friendly and 2 neutral for most of the game, eventually going to 6 friendly and 1 neutral. I sacrificed one of the friendly's to get the 2 neutrals on my side by denouncing the ottomans (who had been denounced by everybody else, including Liz). By this point I had already been denounced by liz as a warmongering menace so I was unable to fix that relationship, but the neutrals quickly came around to friendly terms with me b/c we had denounced the same leader. I was even able to steal 2-3 CS's from Arabia, Siam, and Inca each, though those stolen CS's were spread out over time. I don't know what the threshold for CS competition is, but I suspect that it is higher when you're friendly than when you're neutral or, especially, hostile.
So, to get a more positive diplo rating with a specific civ, you can make a DOF with them, you can make a DOF with a leader that they already share a DOF with, you can denounce somebody they've already denounced, and you can liberate their captured workers. I haven't liberated an actual civ lately, but I assume that resurrecting someone from the dead gives you a pretty hefty diplo bonus with them as well.
They don't dislike everything:
They like it when you give them OB/Trade it with them.
They like it when you give them help during a DoF.
They like it when you abide by your agreements to stop buying land/settling near others.
They like it when you keep your word.
They like it when you denounce people they've denounced.
I've never seen an actual positive modifier for OB/Trade, giving help during a DOF, abidinb by agreements, and keeping your word. Are you saying that those things offer an actual positive modifier? I think that you have it wrong, my experience is that OB/trade means nothing, NOT helping them after you made a DOF is a negative, and lying to them is a negative. So everything you listed other than denouncing the same civ is an opportunity to case the other civ to hate you if you don't do "correctly".
I think most of the people who've said they understand and enjoy the Civ V diplomacy system agree there aren't enough effective ways to positively impact (or repair) your relationships with the AIs, and would like to see some more options there.
As opposed to the haters, who are apparently unable to concede, well, anything at all, to the point of even making stuff up to hate about the game.
I think that this is key. The things that JoeBas listed SHOULD, imho, be positive modifiers, but instead they are just opportunities for you to piss off the AI. Don't get me wrong, I often deliberately do things to piss off the AI so that he gets the warmonger hit for declaring on me, but it's definitely a minefield if you want to play the diplomatic game correctly right now. Hopefully, the new patch will introduce more positive modifiers like "our open borders bring us closer together", which would encourage even high-level players to look at using mutual OB instead of just selling them every single time. Or maybe the old standby "our years of trading bring us closer together". And what about outright bribing them, leading to "your gold gifts bring our peoples closer together" or "you gave us tribute". I realize that many of these are outright stolen from civ4, but a couple of them could bring more diplomatic wrangling back into vogue.
I'm 1st and Siam 2nd), am allied with only 2 CS's that are near my borders and for a long time now. Still, my best buddies are GUARDED and every now and then some civ dennounces me.
