Here is a list of all characters with moves that will generate an item that other players can grab. I tested all of them in training mode. Unless noted otherwise, none of these will stale:

- **Mecha-Koopa** - Bowser Jr. Down Special
- **Banana** - Diddy Kong Down Special
- <strike>**Crown** - King K. Rool Side Special</strike>
 - This move will stale when used as a special boomerang-style. While it's possible to pick up and throw if you don't get it back, unfortunately K. Rool can't pick up the crown himself to use as a projectile, he just places it back on his head.
- **Bomb** - Link/Toon Link/Young Link Down Special
- **Metal Blade** - Mega Man Neutral Special
- **Bonus Fruit** - Pacman Neutral Special
- **Turnip** - Peach/Daisy Down Special
- **Gyro** - Rob Down Special
- **Tome/Levin Sword** - Robin Specials/Aerials
 - Depending on OP's definition of "special move counting as an item"
- **Holy Fire/Aura** - Simon/Ricther Down Special
- **Grenade** - Snake Neutral Special
- **Wario Bike** - Wario Neutral Special
 - Throwing the bike will never stale, but riding it into people will.

That's all the items that I was able to find, but if I've missed any you think might work, let me know and I can test them out!