Playing without war on higher levels is tough, but not hard to do. What you have to do is have limited wars, not long drawn out ones.
My current game, playing China (my new favorite Civ) on Regent level, I've only had 3 wars. I play very aggresive early, expanding like mad, meeting every AI civ I can and trade like crazy. The other Civ's like you more if you a) trade with them often (even just maps) and b) you don't kick them out of your territory all the time. If you keep kicking them out, they *will* get pissed and declare war.
Anyway, large map, 8 civs including myself. On my continent there was me in the middle, Japan and India to the south and south east, Persian way far north past a lot of jungle so they weren't in the mix. I expanded as much as I could, kept following up settlers with defenders and building a horeseman here and there to get my military up there. Me and India were pretty tight, but relations with Japan were strained. Japan finally declared war when I kicked them out too many times. I wasn't quite ready and new they would wipe the floor with me if I didn't act fast. I contacted old India and gave them some tech to join me against Japan. The agreed and we slowly carved up Japan, me taking a little more then half. By the end of the war I got my rider UU and went into a Golden Age just as the war ended. This allowed me to get a few wonders.
Later on we all met the Zulu and for some reason they declared war on me pretty much right away. I got everyone to go in with me against them. They were on a big island quite a ways away. They never invaded and neither did I. We declared peace soon after. They still hated me. In the meantime I was first to find everyone else and made quick friends. The Germans didn't really care for me (suprise) but I kept them happy by trading luxeries. Zulus declared war on me again and this time I got the whole world to go against them. I loaded up 30 calvary (knowing a strong army is a must in this game), went over and took 4 cities on the edge of their island, getting another saltpeter in the process. I really didn't want to fight anymore and declared peace.
Rest of the game, when I got nothing else to build, I build an infranty or tank and have really built up my overseas military. I have at least 2 big defended cities on every continent. Just recently the French and English went to war leaving a wasteland in between their empires. Lots of good resources like coal and rubber in there. I need extra. Knowing it's good to keep a couple settlers laying around just for this occasion, I moved 3 settlers in with infranty and founded 3 new cities and now controled a lot of extra resources.
France, a good friend, just declared war on me for what appeared to be no reason. Why? Because my new cities control the rubber and coal they used to have until the English razed their cities. They have no other source of it. They *have* to attack me. Since they are the #1 civ and I am #2, let's dance! I am now pumping over my tanks and got all civs but the Zulu's to join with me to wipe out the French. The Zulu's know better to attack me because I have 30 tanks on their island just waiting to attack them.
So, the moral of the story is you *have* to have a strong military and be as large as the AI civs to keep them off your back. Strong culture is a must as well. Once you get it figured out, it's actually quite easy to balance the three, IMHO.