The best move you can make is to work harder at building your relationships with them; share open borders, adopt their favourite civics, stop trading with their enemies, gift them gold or resources, share their religion, and so on, and certainly steer clear of negatives such as making demands of them, engineering trade embargos against them, refusing their requests, etc.
... unless you are playing Warlords, in which case you can make them your Vassal and therefore they have no choice about getting into the wars that you make.
In some cases you'll strike tribes that are itching to get into a war. For instance, if sharing Montezuma's religion and having an enemy of a different faith in your sights, it won't take much to get Montezuma to look at declaring war. Some tribes are usually more willing to join a mutual war, so if you want to try this sort of diplomacy you're likely to have more luck with some leaders than others.
In other cases they fear the opposition that you have in mind, or the opposition is too far away from them and they can't see realistic benefit for their nation in getting into the war, or they are just too friendly with your prospective enemy and there's little you can do to break that friendship, or they're thinking of declaring war on another third party, or they're already in a war, etc. etc. The reason that they don't want to war is often identified by their excuse when you hover over the 'red' option.
Some tribes have very long memories, so if you've attacked them at the start of the game and 'say' razed a city, you may still be feeling their wrath quite late in the game.
I hope some of this is of use. Best of luck.
