Try looking for Raffi on Amazon.com, and it will likely show you some other performers of children's songs as well. There was a trio; two women, one man, who did a TV show, and they did lots of songs like that, but I can't remember them. I just remember a song that they did in Spanish that I just loved about an elephant balancing on a spider's web.
Yeah, that was "Sharon, Lois, and Bram". It wasn't them, or Raffi. I don't think it was a local compilation either and I've found a couple references to the songs I can remember (one a post from someone on a myspace/livejournal type blog saying she was looking for the same, it had no useful info but did confirm that I'm not too crazy)
I'm almost thinking it may have been English. The one poem I definitely remember being read by someone with an English accent but that could have been for effect. There was a tortoise-and-hair story told on the tape too and the storyteller had a vaguely English voice. Since my grandmother is English and she and my grandfather made several trips over there when I was young, and since I think she was the source in the first place, that could be where it's from.