Care Bears: Journey to Joke-a-Lot (2004 Video)
At the start of the film, there is reference made to "flying monkeys" by one of the bears.
Funnybone tells the computer to open "pod bay doors" twice in the movie. Also, the Computer keeps refering to Sir Funnybone as "Dave", and at one point even quoted "I'm sorry Dave, I'm afraid I can't do that". Furthermore, the computer's name, PAL, rhymes with HAL, the name of the computer from 2001: A Space Odyssey
In one point of the movie, Sir Funnybone was lamenting about getting a real henchmen, "a parrot or something". The villain of the movie Aladdin, Jafar, had a parrot named Iago as his henchmen.
DVD release reviewed + footage used