Presently, the only Manaphy that can be shiny, is the hatched Manaphy egg from Pokémon Ranger.
However, the received egg is shiny-locked. The only way the egg can be shiny, is if the egg was traded.
At that point, the player is subject to the standard RNG, in terms of trying to match the Egg Shiny Value (ESV) [based on PID] to the traded trainer's Trainer Shiny Value [based on TID and SID].
Another quirk regarding trading eggs to hatch them shiny, is that they will not be shiny in the hatching animation, but will be shiny in the summary.
This is because the original trainer's TID and SID is on the egg, and the hatching animation used that TID/SID, instead of the hatcher's TID/SID.