I don't have many problems. But then, I'm a basic empire/economic builder that likes to dabble in a bit of war now and then.
Simple trade is more then enough to get "Close". If they are of opposing alignment (and you still want them as a buddy), then trade LOTS with them. Once we both have Alliance, I find it's usually a very simple matter for me because by then, we've been "snuggle buddies" for so long.
Now, on the higher difficulty levels, it might take a lot more then trade. It might take a lot of bribing.