Statistically speaking, Blaze2664 is correct. But I'd also like to point out Shiny Hunter Luna's comment.
The method to obtaining Manaphy is relatively simple. First, obtain the game, Pokemon Ranger: Shadows of Almia. Good game by the way, played it myself. Next, beat the entire game. Yes, to get the manaphy egg, you have to beat the entire game. At the end of the game, you should receive a mission to find the egg. Once you've found it and you've obtained the code for it, it is then possible for you to trade the Manaphy egg to a generation four Pokemon game. Now, you have to trade it to another generation four game. Once you've done all this, whatever method you use to hatch it doesn't matter.
Congrats, you've won yourself a ticket to a 1/8192 chance of getting a shiny Manaphy. And the best part if you fail? You can't reset your game to try to get another one! You have to beat the entire Pokemon Ranger game, again!
I'm sorry if this answer seems pessimistic, but a shiny Manaphy is probably the rarest you can get in terms of shiny Pokemon. I hope this helps. Reason why this happens can be found in Bulbapedia's trivia section: here.