If I am correct, influence is, or can be at least, a determent to allying. If you look at the Foreign Advisor (can't remember which tab), you may find that your close borders earn you a - or a -- instead of + or ++ to the empire's attitude toward you. I'm sure the manual says, but I think influence is more for taking over alien planets than for diplomacy. I tried a diplomatic victory once. My strategy? Build up your economy and research, then when you are ready, give them like 10% of your cash and a high level tech or two every turn. Once they are ready (the step past close, I think), they will accept an alliance. If that is your only objective, don't be afraid to give them every dime and tech you have, even planets, just to be sure. Of course, mine was a metaverse game, and I had all of the diplomacy tree researched, so there may be other ways for shorter games. Try a variation on that first though, see where it gets you.
