I've managed to get the AI to trade a city for peace if they're almost completely wiped out. Sometimes I use it to get an island city that would be harder to invade than the remaining continental cities.
We had this repeatedly tonight with Genghis. Pretty interesting game as Elizabeth; Genghis declared on us (not totally unexpectedly, but with an alarmingly huge stack of Knights given the size of his empire) when we'd just invented Rifling, so in spite of a few turns at 0% science and mass upgrades later, we lost one small city - vexingly dividing the empire, leaving one actually decent city isolated on a peninsula with, er, one Redcoat to defend it (the rest having died in a vain attempt to recover the situation before the loss of the small city) and Genghis's stack a turn closer than the reinforcements coming by Galleon. So... we bought peace with Music, which was generous of him, considering. I suppose he wanted to consolidate his gains and heal troops; but of course ten turns later (when he immediately DoWed on us) there were about a dozen Redcoats waiting to put things right.
You know how this goes; you have a significant tech advantage, the AI declares on you anyway, you give them a solid kicking and steal and/or raze a few cities, they make peace but they hate you forever because you burned down a city or two, they don't catch up tech-wise because they waste all their hammers building inferior units, they declare on you... rinse and repeat until you get fed up and make them capitulate - in this case, I think, on the fourth war, by which time we had Infantry and he still had, er, Knights. And some Musketmen.
Anyway, the point of this whole rambling story is, his cities were universally awful (presumably because he spent all his hammers on Knights; also explaining why we burned them all down when we took them), but every subsequent time we made peace, he was desperate to put a small city on the wrong side of his empire into the deal - which of course we had no use for whatsoever. I've seen it occasionally before, but I've never seen an AI so utterly desperate to give me a city at every opportunity. Anyone know if you're allowed to immediately burn down a city you get as the spoils of war? We didn't accept them because, if you can't, we didn't want the maintenance burden.