Because of the song, some people do try to make them out of clay.

During the Jewish holiday of Hanukkah the usually strict rules discouraging any kind of gambling are relaxed slightly. The dreidel is a 4-sided top, each side inscribed with a letter. The letters form an acronym that reminds the players of the meaning of the holiday: <[a] Great Miracle Happened There>, roughly translated. The top is spun by children to win small treats such as chocolate coins. The dreidel is symbolic fun and of the holiday period but carries a serious message at the same time. Dreidels aren't supposed to be made of clay; they are usually wood or metal--& nowadays plastic. It's the translation of an old song which falsely mentions clay. That's not a mistake, however. The top in the original song was made of lead; not something you want to encourage kids to play with today.