Yes, there is a Shiny Palkia, but it is extremely difficult to capture.
Here are a few methods you could go by to get the Shiny Palkia:
1. Hack with a GameShark/Action Replay. (Not recommended as it won't be considered "legit.")
2. Go to the Global Trading System and trade it for something of equal value.
3. In the encounter in Pearl (I'm not sure how it is with Platinum) save after you have defeated Commanders Jupiter and Saturn. Run into Palkia and, if it is not a shiny, reset your game. Keep doing this until it's shiny.
The reason why method three works is because the game randomly rolls a dice when you start a battle (this occurs when the screen is black and the theme song of a battle starts to play). If the dice reaches a certain number, the Pokemon is shiny. However, method three can take anywhere from one to a million tries, as it is by pure luck that it will be shiny.
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You can get a shiny Palkia in Pokémon Pearl by doing a soft reset in front of Palkia before fighting it. Do a soft reset by holding L+R+Start+Select.
Very rare
smell flute!
the difference is that the color is differint(shiny mew=blue, shiny palkia=light red shiny deoxys=yellow shiny porigon2= all blue(different shades)) and at start of battle, makes a sound.
because it has pearls on its arms. ...wait is this a joke ? because it has pearls on its arms. ...wait is this a joke ?