While working on Avenue Q, I was also comissioned to make a mock Oscar the Grouch "puppet" to live in the trash can onstage as a fun little nod to the show's inspiration.
The base of his head is a paper mache'd balloon, which I patterend and covered in fur. The rest of him is fabric. He attached to the lid of the trash can with fishing line and was folded inside, so that he appeared to pop his head up when the lid is lifted.
These DIY ornaments are one of my favorite supplies for puppets and masks. They're clear plastic, come in a small variety of sizes, and are already cut in half but snap back together easily. If you paint the insides you maintain a nice shiny finish that looks great for characters' eyes! The only issue is you'll only find them in-person at craft stores around the holidays, but I'm sure they're avaliable online year-round.