The special, which is based on some book called "The Easter Bunny That Overslept," starts in the magical land of April Valley, which I'm assuming is a reference to Baum's "Laughing Valley." Either that, or it's just stupid. Regardless, all the Easter Bunnies live in April Valley, where they color eggs using paints brought to them by Seymour S. Sassafrass, who grows the plants to... you know what? Let's simplify things: Danny Kaye sells them magic paint.
At any rate, the chief Easter Bunny is getting ready to retire and needs to choose a successor. He settles on Peter for absolutely no discernible reason, but the evil Irontail talks him into a contest instead: whoever delivers more eggs becomes the undisputed ruler of the valley. Irontail is voiced by Vincent Price, and - just as his name implies - he has a metal tail. Also, he wants to abolish Easter.
After sabotaging Peter's alarm clock with gum, he wins the contest. Peter leaves in disgrace, vowing to somehow make things right. This is when Danny Kaye reenters the picture: Peter winds up in his garden and explains his predicament. Kaye then gives him access to a time machine piloted by a caterpillar speaking in a French accent, also voiced by Danny Kaye.
For the record, this is when things start to get weird.
The aforementioned time-machine is essentially a time dirigible. When we're introduced to the machine, we're shown it has buttons for all the different holidays. The plan is to take it back to Easter, so Cottontail can win the contest. Things go horribly wrong (mostly for the viewer) when Irontail realizes what they're planning and sends a hench-spider to break the machine's controls. The time-machine goes out of control and starts crashing at other holidays.
At this point, any semblance of logic or continuity is pretty much out the window. I honestly can't tell you whether they were going forward or backwards in time through this thing: frankly, neither makes sense. They can't be going forward, because Peter is still able to win if he's able to give away his eggs. And they can't be going backward, because Irontail remembers their prior interactions.
Ultimately, it's all just an excuse for Peter to run around other holidays trying to give away repainted Easter eggs. There are stops at Mother's Day, The 4th of July, Halloween, Thanksgiving, Christmas Eve, Valentine's Day, and Saint Patrick's Day before Cottontail makes it back to Easter. The Christmas section features a crossover with Santa Claus, who is far more interesting and better designed here than Peter.
Ultimately, Irontail uses dark magic to turn his eggs green on Valentine's Day, so no one will want them. After a quick stop at Saint Patrick's Day, Peter is victorious. Again, provided you buy the contorted temporal metaphysics at work here. Also everyone learns an important lesson about lying or something.
I actually remember a time when the idea of watching a Rankin-Bass special I'd never seen before was exciting. That was about eight stop-motion fiascoes ago. Turns out, there were really only a handful of Rankin-Bass specials that were any good, and (how honest are we being here?) even those are kind of tedious now. But at least Rudolph and some of the Santa specials seemed innovative: this is just a contrived mess.
Okay, okay. I'm being a little too hard on this. There was some good animation, particularly on Santa Claus. Also, it's certainly an impressive voice cast. But that's nowhere near enough justification for sitting through this.