If you can manage to no longer border them through rebels or another country colonizing them, you stop paying tribute. And if the horde manages to stop being a horde (revolutionary rebels or forming the Mughals) tribute stops.
Yep. I mean, technically, bankruptcy might do it, if you're prepared to go that far, but unless you declare war on a horde (or somebody else wipes it out for you), you'll pay tribute the rest of the game.
OK, that helps. Thanks!