Directly mentioning diapers, no…
Some games, though, hint them based on context. For instance, Metroid, Samus is inside her Chozo Suit the entire adventure, so, like astronauts, she may be using a diaper, same goes for Master Chief.
Tomb Raider (the original one, on the playstation), most due technical limitation, makes Lara looks like she's wearing a diaper, when I'm playing, I like to think she is caring spare diapers in her backpack.
The recent Mario Kart titles have baby characters, personally, I'm not into toddler stuff, but it is worth mentioning.