The easiest way to get this is boosting. The Rotten Apple card unlocks at 5 online wins, so be sure someone in the party has it unlocked to use on everyone.
If you're not boosting, this could be a very long wait, as it's dependent entirely on the choices of other players. You might be able to speed things along by playing Golden Apples on other players - steal enough points and you may annoy them into wanting you not to play anymore.