Do you specifically want to know how the muppet's did it, or in general how one would do it. If it is the latter, I just made a pupet with a 2dimensional uvula tonight. I covered the mouth plate in black belt, then cut another covering out of dark red felt. I cut out the negative space (in other words, the hole, leaving the uvula as part of the red felt) and there you go, a cool throat pattern.
Now my question is, what's the best tongue placement- insid the hole, outside, on the edge? I tried looking at some muppet pics for inspiration but couldn't get a clear look.