Title Help- Old Movie With A Bunny?

My Dad told me about this movie he saw when he was young about this guy who has an imaginary bunny friend who he talks to (played by a guy in a bunny's suit) - He told me about it when I had tried briefly explaining to him what Donnie Darko was. My Dad was born in 1948, so I'm guessing this was a movie in the 50s-60s range maybe? I can't remember the title, if it was something the bunny, or my friend something... If anyone knows I'd really appreciate it! Thank you!