Will shiny Pokemon appear when playing Pokemon Rumble on an emulator?
Solution 1:
According to the Dolphin Emulator Wiki, there are no reported problems with the title. And, according to Bulbapedia, a Pokémon wiki, "Shiny Pokémon may rarely appear. They will always tip over when defeated. The chances of their appearance are unconfirmed, although they appear to occur more often than in the core series."
This seems to just be a case of really bad luck in your case. Unless your copy of the game is faulty, shinies should still appear, as Dolphin Emulator does not adjust any properties of your game.