Diplomatic skill has no effect on the strength of an alliance. Neither does civilized vs barbarian.

Two tips:

Never make an alliance with a faction you have a common border with. That is tantamount to a backstab and an invasion. Only if you have local overwhelming superiority will this not happen.

Never, never, ever make an alliance with the Greek Cities. They are the biggest back-stabbers in the game, bar none. I once saw them switch sides three times, attacking their former allies TWICE!