I usually find that a perceived position of strength is beneficial in negotiations, including peace treaties. Normally the AI will only accept deals where the AI makes out. However, if you move a stack of units next to one of its cities, the AI will sometimes give you a good deal, in the hopes that you will be satisfied.
I was exploring the world, and simply moving a caravel next to an AI's city was sufficient for it to give me a great deal! This was after I said I was moving my units away from his territory. (They were the Greeks)
I've had wars where I've pretty much decimated the other side's offensive capability after several turns. I imagine the war weariness was starting to kick in, and they gave very good terms (a technology advance, 3 workers, and gold/turn for a peace treaty); right after I moved a decent sized stack next to one of their cities.
Another strategy for making deals early on: at monarch level I find myself behind technologically. I build a bunch of veteran warriors, start a war, take a couple of cities to show I mean business. After moving in on the capital, I offer a peace treaty for all their technology; this is often accepted. I then take them out anyway! (What do you expect from a despot?)