According to what I've heard, if AIs have 3 or more alliances, they won't accept any proposals. Not sure about the player himself/herself.
A long time ago this was a hard limit, now its a soft one.
That is if you have good reputation, good relations and a great deal of trust between the country your trying to ally and yours, and they have 3 alliances, they may still accept a alliance (likely with low chance though) if you dont have many yourself.
You tend not to be able to acquire alliances except by diplomatic action if you have a great many (released nations, vassals, unions ect).
But in his case... Likely he has tried good reputation, and good relations with few alliances... So the only thing you can try is trust. (something i always stress as really important long-term but see people not actually care much about). You can raise it by like.. guaranteeing people and then helping them defend themselves from attack (and for god sakes you should always honor calls from allies unless your going to suffer a massive defeat if you honour it).
Oh i forgot to mention, people like to ally people around the same strength as them.. so if your 1/10 the size, its not likely going to happen naturally..