If I play a Stadium card on my turn then on my next turn I play Dark
Vileplume on my turn do I have to discard the Stadium or does it stay in play?

A question brought to you by Methane Man.

Dark Vileplume states that you can not PLAY trainers.  Stadiums are cards that are already in play when Dark Vileplume comes down, and their effect will continue as long as they remain in play.