The AI will continue to desire war with you until you offer them some enormously advantageous trade deal, or they're fearful that they will lose territory to your military.
Personally, I don't think it's worth it to pay them off, especially if you're in the situation where you think you're stronger than they are.
Luckily, the AI is terrible at war. Just stick some ranged units (ideally something like Catapults, Trebuchets, Cannons, etc) in your border cities, with some melee units in the hexes towards their border. They will roll up and get slaughtered, significantly reducing their military might. Eventually they will come and beg for peace, and offer you something terribly lopsided in return.
If they are distant enough from you, chances are you'll only see a few units or a meager trickle. In this case, they're never going to get weak enough to offer peace, but they pose such a tiny threat that being at war is not that significant. Just ride it out, and eventually something will come along that requires their attention. At that point, they'll probably make an even offer for peace.