Pokémon Channel is a game for the GameCube, and Jirachi was introduced in Generation III (Ruby, Sapphire, and Emerald). While the games are in the same generation, Pokémon Channel doesn't have the mechanics to obtain Pokémon from other games.
Jirachi was later made available in other games like Pokémon Colosseum and XD Gale of Darkness, which also featured the Generation III Pokémon.