I have only used this with two-year-olds in a Mommy and Me class I teach, so I don't have much in way of a rhyme to use with Cookie--yet. The two's just love bringing up their cookie to put is in his mouth (Love with a dash of fear. He is a monster, and that is a big mouth). After each child added a cookie, we all said, "Yummy, yummy in my tummy!"
Cookie is about 20 inches in diameter, so we had some more fun with him after circle time. I put him on the floor on top of a large piece of felt with cookie sheets on either side. The kids threw round felt cookie bean bags at the assortment of targets. I can't sew, so I just hot glued two beige circles together, filled with beans, and drew on chocolate chips. It was all super simple and very fun.
See the original post if you are interested in a craft to go along.