Happy Animals' ABC (Book, Helen Wing & Racey Helps, 1980)
You can digitally borrow it here.
Untalkative Bunny - The Complete Series (Videos, 2001-2003)
Holy crap I think they found it. The whole thing. aaaaaaAAAAAAAAAA watch it here.
Dyna the Dynamiter Rabbit (DOS, Frodo/Sponge Productions, 1997)
You can play it in your browser here. Reading the instructions is a must.
Super Bunny (In-browser, Apple II, Datamost, 1983)
You can play it in your browser here. Controls: arrows. Time your jumps, grab the carrot on the right and clobber the enemies!
Happy Ending Stories (Videos, 1986)
Adorable children's VHS tapes for helping deal with childhood fears. Find them here - they're in a zip file, the files inside which are listen and downloadable here. All videos are under 70 MB (except the optional combined video of episodes 7-9).
These were based on a series of children's books - here's some of them, digitally borrowable, along with some others by the same author, Jane Carruth.
Farm Animals: Close Up And Very Personal (Video, 1991)
You can watch it here.