Question

What are the items the Pokemon need to breed that won't breed unless one of the parents are holding an item?

Answer 1

There are no Pokemon that need to hold items to breed, but some baby Pokemon will not hatch from an egg unless the evolved form of the baby Pokemon is bred while holding a specific item. For example, if a Marill or Azumarill is bred when it is not holding a Sea Incense, the egg will hatch into a Marill. If a Marill or Azumarill is bred while holding a Sea Incense, the egg will hatch into a Azurill.
Listed below are the Pokemon that must hold an Incense in order for a previous evolution that is a baby Pokemon to hatch from the egg produced.
Marill/Azumarill must hold a Sea Incense in order for an Azurill to hatch from an egg produced by those Pokemon. Snorlax must hold a Full Incense in order for a Munchlax to hatch from an egg produced by a Snorlax.
Wobbuffet must hold a Lax Incense in order for a Wynaut to hatch from an egg produced by a Wobbuffet.
Roselia/Roserade must hold a Rose Incense in order for a Budew to hatch from an egg produced by those Pokemon.
Chansey/Blissey must hold a Luck Incense in order for a Happiny to hatch from an egg produced by those Pokemon.
Chimecho must hold a Pure Incense in order for a Chingling to hatch from an egg produced by a Chimecho.
Sudowoodo must hold a Rock Incense in order for a Bonsly to hatch from an egg produced by a Sudowoodo.
Mantine must hold a Wave Incense in order for a Mantyke to hatch from an egg produced by a Mantine.
Mr. Mime must hold an Odd Incense in order for a Mime Jr. to hatch from an egg produced by a Mr. Mime.

Source

Comments

"Unless a Pokemon is bread while holding a specific item."

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Yes, breading. It's when you're pelted with bread. That's exactly what I meant.

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it means, it has to be holding the item at the same time as becoming a lovely loaf. but seriously.
have you proofread this? I don't think a mantine produces a Whynaut.

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Thanks for pointing out my errors! I copied + pasted "Wobbuffet must hold a Lax Incense in order for a Wynaut to hatch from an egg produced by a Wobbuffet." so I didn't have to type the same thing over and over again, and I knew that I would forget to replace one Pokemon's name with another and end up looking stupid. Guess I was right.