I entirely agree with you there. The diplomatic victory is poor. I believe the real problem with quests is that sooner or later they all end up being "wipe this city state out", which the AI (and I) very rarely do because its not worth the larger repercussions. I would like to see more of the "hook up this or this resource", because that would force you to actually be diplomatic with other civs. I also think having a "gift us this unit" quest could be quite interesting and easy although still a considerable investment. I also think a nice quest could be "become friends with City State X", which could lead to some interesting dynamics. More importantly, they need to have a time limit of maybe 60-80 turns, so that the games doesnt get stuck on quests that arent worth it.
Lastly, the amount of gold you need to buy influence should increase with eras to balance it out. In the early eras it needs to be reduced, because at the moment theres no point in killing barbs for city states because the influence never goes high enough to make a difference for long. Gold should be the last measure to increase influence; not the main one.