I have 2 ideas:
Egg Swap Challenge
- Once 4 or more people join the challenge, all the participants egg swap 5 eggs with each other and trade them to whatever game they are playing to hatch them.
-This could work on Gen 4/5 easiest but could also be done with just regular trading in VBA Link.
Not My Pokemon Challenge
-This challenge would be done by only using pokemon you receive from other players in the game. This includes Gift Pokemon, traded pokemon, egg's that the player is randomly given, and I bet there are a few more circumstances.