I don't play a lot of games, basically one after the other, only multiplayer. With the latest modpack version (10-9.1) on a small, continents plus map on Prince level, I have both been offered defensive pacts and was able to easily bribe an AI civ into war to fight by my side. I have to say though, that I'm doing quite well in this game, basically leading in all areas (science, religion, culture, gold) except for military (my science advantage of 5-10 techs might make up for the numbers, but I only have about 10-15 units that actively participate).
What happened was, that I declared war on civ1 (Dido) which had a defense pact with civ2 (Napoleon) (both civs were comparable in score to me before the war). After a while, I realize that both are too much for me to handle, manage to make peace with civ2 (defense pact must have run out), continue my war with civ1, bribe civ2 into joining me in fighting civ1 for as little as two luxury resources and eventually take 4/8 of civ1's cities before going to peace.
Altogether, I had the feeling that the AI did a good job at sucking up to me once I had finished that war and consolidated my empire. Shortly after, AI civs would start to offer me friendship and even a defensive pact. In addition to this, I've gotten much more secure in negotiating deals, i.e. declining AI offers and requests while pushing my borders into their terrain, demanding tribute etc. The AI accepts all of this and seems to be happy to be my friend. What does surprise me though is that Dido went right back to friendly once we had made peace. That does sound a bit like Stockholm Syndrome to me but OK
This is of course just a snap shot and I've certainly had games that went about much differently, but I think it's an example that everything is possible given the right circumstances. I guess we have to accept that the way the AI assesses certain situations is just different (unbiased?) from how a human player does it.
Assorted things I noticed:
1. Sweden (reduced to a single city by another human player) would offer me Open Borders (the only thing they had really) almost every single turn for things of much greater value such as lots of money, resources etc. Their deal value was always in the hundreds but they didn't seem to understand this.
2. Every once in a while the AI would offer me deals with a single digit negative deal value, so that they wouldn't accept their own offer.
3. One of my scouts was turned into a zeppelin through a ruin. At least that's what I think must have happened. It was set to explore and at some point it was a zeppelin. I don't think that makes a lot of sense.
4. Barbarians were totally fine. Not too aggressive (not a fan), not too docile IMO.