In Pokemon Colosseum, if one of the few Shadow Pokemon you can catch in the game happens to be shiny, it’s extreamly unlikely that it will retain it’s shiny status once you catch it, because the formula the game uses to determine whether a pokemon is shiny or not uses the personality value of the Pokemon and the Trainer ID of the trainer that sends it out at first, once you catch it the formula is re-calculated using your own Trainer ID. This can also potentialy work both ways and make a normal Pokemon into a shiny pokemon once you catch it.
In Pokemon XD, none of the Shadow Pokemon in that game can ever be shiny, since the game will re-generate personality values for the Shadow Pokemon until it is not shiny, however the Eevee you have at the start of the game can still be shiny.