No, there are no Pokémon diapers. Pokémon don't usually wear clothes so there's no need for diapers, plus they can control their bowel movements. There might be a way to tell but that would mean scanning through the whole (640+) Pokémon anime series (cartoon) to see if there were any episodes with Pokémon wearing diapers in any day-cares.
Don't want to take my word for it then happy searching and good luck...
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Yes, there is a mod that allows all ages to wear diapers.
jars of Gerber Baby Food The Genie (item to buy for disposing of dirty diapers) Good Nights brand diapers
bib diapers booties onesies
diapers Desitin diaper rash
Diapers, Dad (not an item, but essential for a baby).