I forget which game it was, but you could ask for a mutual declaration of war as a treaty. If the AI is small and its opponent it hates is big, then it would benefit from being a weighted possibility in its calculations. Hates not dislikes should be the condition, as its an even more threatening move than a straight declaration of war, and for the player might see the removal of said race, not just fighting to a peace.
The reason this is superior to the traditional, please join us in our war, is because it instantly means two, three or more threats quite possibly from different directions, which takes some thought from the player or effort from the AI to counter, in fact distance from the AI but proximity to the target might make a better choice to open up these multiple fronts.
As a side note, I don't know about you, but the very turn someone declares war on me and I think they might have the upper hand, I always get another race nearby them to go to war, that turn if possible, I don't wait till half way through the war, and I am willing to be generous in trading to get it.