In Pokemon Legends: Arceus, they have a quest where you can get Manaphy and Phione, and catch them, actually. You have to accept "The Sea's Legend", quest first, and you have to swim through the two pillars of rock in the Cobalt Coastlands with Overqwil, Mantyke and Buizel in your party. Then, you have to go to the Seaside Hollow, in the cliff face by the Islespy Shore, and fight a whole gang of Phione guarding him, catch them all, and Catch Manaphy(the Phione all respawn, but Manaphy doesn't, so don't OHKO it on accident!). Then, report back to the Professor, and register both to your pokedex.
You can also get Manaphy in Gen IV by completing the spinoff game Pokemon Ranger and transferring the gift Manaphy Egg to a Gen IV game.