Sarah McLachlan did a cover of that song. YES SHE DID A COVER!
I found it on one of my various music communities that I am joined to over at tear_venus (Name is an obscure reference to some RPs I've been in)
The Rainbow Connection by Sarah McLachlan.
The Rainbow Connection by KERMIT THE FROG
Compare if you want.. *heh's*
That is why I loved the Muppets.. because they were definitely not for kids, or maybe it was just geared toward kids in the 80s. Who knows. I just recommend you download them.