You can't lower their tourists that they already have, but you can slow them down (and also increase the domestic tourists they need to overcome)
Tourism is generated mostly through great works, artifacts, and sometimes wonders. Later on it comes from seaside resorts too. The holy city generates a bit, but it's not that much later in the game. And they can move works out of a city under attack, thus the only way to really do is to take their cities with theater squares and also force them to cough up great works in a peace treaty
You can also opt to use a spy and steal their great works, as well as denying them open borders or giving them trade routes (which boosts their tourism). You can also wipe out nearby civs so they can't get tourism off them.
Peaceful methods include propping up whoever has the strongest culture (besides them of course). When it comes to a culture victory, all that matters is that the winner's tourism exceeds the best culture (that isn't theirs); so only the civ with the best culture actually matters when opposing them. Obviously as many people hate or denounce or war with the one you don't want to win a CV will help immensely too.