The Easter Bunny Is Comin' to Town (1977)

The Mailman decides to stop another deluge of letters by answering questions about the Easter Bunny: Sunny, a baby rabbit found and adopted by Kidville (a town of only kids--even a kid mailman). And when Sunny goes delivering eggs to the nearby town (which he has to dye to fool Gadzooks, the mean bear on the mountain), he discovers that there are no kids in the town, and that the rightful (kid) ruler is being suppressed by his aunt. But the young king likes Sunny's dyed eggs and jelly beans. So Kidville, with the help of an old train engine, makes a few plans (and a decoy chocolate rabbit) to distribute them.