The Pokemon that can learn yawn, protect, and belly drum are the Slowpoke family, Snorlax, the Teddiursa family, Smeargle, the Spheal family, the Darumaka family, and the Swirlix family. Of these Pokemon, the fastest one is Darmanitan.
source (using /ds in a chat room)
While this strategy is possible, I can't recommend a moveset to exploit it because it's a bad strategy. First, the opponent can switch out when you're using protect, and in the process get a free turn and avoid letting a Pokemon fall asleep. Second, the opponent can switch out when you're using belly drum, and in the process get a free turn and preventing you from trying again (if you're playing with sleep clause). Third, your opponent can let you defeat one if his/her/its Pokemon, take advantage of your low HP, and revenge-kill you. There are plenty of better strategies. Don't try this one.