The Monkees recorded a version of "Cuddly Toy" in April of 1967. It appeared in November 1967 on their Pisces, Aquarius, Capricorn & Jones Ltd. album.
Pandemonium Shadow Show which contains Nilsson's version of the song was released a month later.
The Monkees version was performed twice on their TV show (during the episode "Everywhere A Sheik, Sheik" [9-25-67] and the episode "Monkees On The Wheel" [12-11-67]).