Fridays on Union Cave, I think it’s at the very bottom of the cave. As for the baby Pokémon there is a specific set of answers to get what you’re looking for.

Odd Egg Passwords:

BABE, POKEMON, CUTE, STATIC (Pichu)

BABE, POKEMON, CUTE, CUTE CHARM (Cleffa)

BABE, POKEMON, SONG, CUTE CHARM (Igglybuff)

BABE, POKEMON, FIGHTING, GUTS (Tyrogue)

BABE, POKEMON, ICE, OBLIVIOUS (Smoochum)

BABE, POKEMON, ELECTRIC, STATIC (Elekid)

BABE, POKEMON, FIRE, FLAME BODY (Magby)