Here is a list of all characters with moves that will generate an item that other players can grab. As I don't have a switch with me, I won't be able to test some of them to make sure that the staling properties work as expected. I'll be updating this answer in a few hours when I'm back home.
Bowser Jr.
- Koopa - Down Special
Diddy Kong
- Banana - Down Special
King K. Rool
- Crown? - Side Special (Maybe only when it's been grounded? This needs to be tested...)
Link/Toon Link/Young Link
- Bomb - Down Special
Mega Man
- Metal Blade - Neutral Special
Pacman
- Bonus Fruit? - Neutral Special (Needs to be tested for staling properties)
Peach/Daisy
- Turnip - Down Special
Rob
- Gyro - Down Special
Robin (Both of these depend on OP's definition of "special move counting as an item)
- Tomes - All special moves
- Levin Sword - From overusing aerials
Simon/Richter
- Holy Fire/Aura - Down Special
Snake
- Grenades - Neutral Special (Needs to be tested for staling properties)
Wario
- Bike - Side Special (Needs to be tested for staling properties)