I like Prankster users like Whimsicott. It has access to both Taunt and Encore, I think, and Prankster gives those moves priority. Combine that with U-Turn to give your team some momentum.
Whimsicott (and almost everybody else) also has access to Toxic, which will put a timer on every opponent who can't come up with a way to erase the status condition.
Other pokes with Prankster include Mega Banette, Sableye, and Klefki, off the top of my head.
I think phazing moves would help, too. Things like Dragon Tail, Roar, and Whirlwind will force the opponent off the field and undo any status buffs they just did, hopefully disrupting their plans. These moves have negative priority, meaning they're usually guaranteed to go last, so be careful.