Billy Bunny, I remember that guy! He was a Muppet character from the mid-90's, yeah? Was he ever on Muppet Tonight? I do know him, though. He was on sing-along Muppet videos, including briefly on the "It's Not Easy Bein' Green' one (he did a song with all these frogs). He was performed by Kevin Clash (Billy's laugh is identical to Elmo's)
Frog: "Arn'cha gonna sing, rabbit?"
Billy: "I thought it was ribbit"