How about a Rockford or Bridgestone Chibi (means "short")
You know, I think that's it! I'm kind of shocked that it is so small, but I guess I was small then too. I do remember that it was smaller than my friend's big brothers' dirt bikes. Looking at how far the seat hangs off the back, I can easily see how two kids on there could get the thing to wheelie & dump it's riders off the back.
I couldn't convince myself 100%, but then I searched, found pictures of the right blue, and then there was a video of a restored example running. The sound did seem just right, I'm pretty sure this was it.