Recent Game
OK, I'm having increasing success with the AI, it would seem. In a recent game as France (King, Continents, Standard settings), I engaged in two very short wars with Songhai rather early on. Askia had settled right in the heart of my prospective lands and after antagonizing him for many turns so I wouldn't be the aggressor, I gave in and DoW'd. Once I had the city (took two wars because it had very high defense and I needed swords/muskets), I sued for peace and never went to war again for the rest of the game. Once I met Siam about mid-game, I managed to forge a Defensive Pact that was renewed repeatedly until Siam launched for a space race win. In all, it was a pretty weak showing for me, with the diplo success being the only positive aspect.
Current Game
My current game (Askia on Prince, Continents, Standard) is *much* more interesting and tricky diplomatically, but all in all, I think I've managed things quite well (although I think I'll again lose my culture-win bid to a Darius space race). Here's the scene (a bit detailed, but it truly feels like an intricate, interwoven web, with each fiber being critical to how this has all played out):
Me, Monty, Wu, Suleiman, and Rome occupy a mid-large continent, and we're pretty evenly distributed (i.e., equidistant from one another). My starting location is in the heart of some *fantastic* terrain on multiple levels, but especially defense wise. To the west and south lay the sea. There are great choke points all over the place in the northeast of my core empire, with an eastern buffer of three tiles of marsh, then a river, then a maze of mountain ridges (Maze Mountains?), then Seoul, and then a vast desert in the center of the continent all buffering my northern-most city from attack from the east. Edinburgh is due north of that city, with a large sea inlet north of them. The entirety of my core empire’s eastern border is flanked by a long mountain range (which extends south from the marshlands to the north - Eastern Mountains?). The southeast border is the most “exposed,” with a 2 - 3 tile-thick range of hills extending south and east from the southern edge of the Eastern Mountains on my original eastern border.
OK, so Rome starts to my north. Sully starts due east of me on an inland sea in the heart of the continent. Wu is in the far northeast, and Monty starts to my southeast, more or less directly south of Sully.
Sully of course wastes absolutely no time before plopping a settler right in the heart of my prospective lands (just like Askia did to me in my last game...and now I'm Askia...coincidence?!

). I ask him not to settle near me, but he basically laughs in my face and plop goes the city. So, I warrior rush him, take it, make for his capital, and then ask for peace once I'm in place for the final assault. He accepts, and peace reigns for awhile.
Fast forward a ways, and now I have swords with Chivalry on the way (I think this might actually be important). Rome has warred a little with Wu to his east and has also expanded rather quickly to the south, and now has a desert-encompassed city with river/flood plains due east of Seoul. Next thing I know, Rome DoW's and moves west through Seoul's territory and the Maze Mountains only to cross the river into the marshlands east of my northeastern city. My archers tear his units to pieces and my horseman and swords clean up any stragglers. Rome offers a cushy peace settlement and on we go.
Fast forward again: I have Steel and Mandekalu, with Gunpowder on the way. Rome DoW's again (really starting to think the AI is anticipating the effects of militarily-significant techs), this time bringing a rather anemic Sully along with him. I take Istanbul and another of Sully's cities, the second one being on the inland sea due east of the Eastern Mountains. It also happens to be directly south of Rome's desert floodplains city. As a result, Rome asks for peace when I take that second Ottoman city, but I'm sick of his aggressiveness, so I take his desert outpost (actually a nice location), and then get another cushy peace deal. Awesome.
All this time, by the way, Wu and Monty have been keeping everyone at arm's length and staying out of the fray, although Monty is starting to get more belligerent around this time (I suspect due to a PoS and/or PoC with Rome). When the Songhai-Roman-Ottoman war is over, however, Wu dives in, taking the last two remaining Ottoman cities. A period of relative peace then settles over the continent, and I start laying some diplomatic groundwork aimed at preventing further wars. I secure pacts of secrecy with Rome, Wu, and Monty against one another, except Monty wouldn't go for one against Rome. I'm then able to trade with each without seeming to upset the others (Monty being left out so I don't annoy Rome).
Well, go figure that as I am researching Rifling, Rome comes back for more, bringing Monty along with him. This is actually very bad news, because I have my army split between the city I captured from Rome and a new city I founded near Monty's northwestern border. I managed to hold off Rome for quite a long time with a catapault, archers, Mandekalu, and a couple longswords, but ultimately they managed to surround and overwhelm the city (via quite competent use of pikeman, longswords, knights, archers). Meanwhile, in the south, the hills are really helping me on defense. It gets dicey, but I hold on, upgrade a longsword to a rifleman, drop a citadel on the border, and Monty eventually gives up. Around the same time I bulb chemistry, purchase a cannon, a rifle gets produced, I upgrade another longsword, and bring the rifle from Monty's border up to the city Rome had just recaptured. It's not long before I have that city back and secure yet another cushy peace deal from Rome. I’d like to note here that only once, during the early phase of that last war, were my goals as a builder in anyway affected by war. The topographical features make my strongest cities almost utterly unassailable, and so, other than needing to crank out units to replace those lost in defense of Rome’s old city, my core empire has been essentially unscathed by war since the outset.
OK, anyway, now is when the diplo success really starts to get rolling. Once this war is over Monty is looking a bit like a whipped dog, but he’s dropping hints. “Your empire is famed for its strong economy…perhaps someday you’ll share your secrets…”. I take this as a cue, and as soon as I have the money, I offer a PoS against Rome and an RA. He bites. Cool. I visit the other leaders again, and this time I actually manage to get a PoS from each against the other two. A little while later, I get Monty to DoW Rome. It doesn’t last long, but then Wu and Monty go to war, and Monty starts to get the upper hand. I start to fear that I’ll lose continental supremacy, so I put feelers out to Rome to see if they’re interested in more war. They are, for the price of some of my abundant Gems (I have 7 sources). Fantastic! So, now all of the other civs on the continent are at war.
Enter Darius and Ghengis. There’s not too much to say about them, other than that Darius is a freaking behemoth (I’ll probably lose to his space race bid), and that *both* are all too happy to maintain ongoing defensive pacts and RAs. As soon as I set these up, Rome becomes visibly disgruntled in all our dealings. I love it. He used to talk about his plans for world domination, and now he just shakes his head bitterly when he sees me.

At one point he tried to get me into war with Wu, I said, “give me 10 turns,” then bailed, but he seems to feel powerless to do anything, lest he go to war with the two massive empires across the sea. So, as it sits, there is a continental war going on that consumes everyone but me. I may have to jump in to slow Monty down a bit, but that would be a bit counter to my diplo strategy, so I’m a little hesitant. I don’t think he could be beat me in anyway other than score/time, so I’m not sure it’s worth it.
Anyway, I consider this successful, because I feel as though I was able to manipulate a map full of aggressors into refocusing their aggression from me to each other, and then reinforce that situation by being the first to find and make diplo inroads with the new world.