Obligatory mention of Flygon because it's one of my favorite Pokémon and I love it~
I would love to cuddle an Absol! They try to warn people of incoming disasters, only to be condemned as harbingers of the very misfortunes they seek to mitigate... I think they're entitled to a little TLC, hehe~
Any member of the Cyndaquil line! They just look like they'd be super soft, and warm due to being Fire-type. I'd imagine that Quilava in particular would also be really floppy and maybe rag doll-like to pick up! Typhlosion may have similar flop properties, or, "Floperties", but it's pretty heavy and harder to lift~
Also, Mewtwo, but only after becoming very close friends with one and earning their trust. Sapient artificial bio-weapons deserve love, comfort, and affection, too!
Really, there are many more than this, but these are the standout ones, hehe~