Besides the one for the legendary dogs.
It is impossible to get a Shiny Mystery Gift Pokémon, UNLESS it is meant to be Shiny like the Pikachu-colored Pichu. This is because in the game's coding, there is a Shiny check function which prevents Mystery Gift from being Shiny by regenerating a new PID until the Pokémon isn't Shiny.
Source: Bulbapedia