DeepDish 622,
I have seen non-metal deep-dish pans advertised over the years at King Arthur and elsewhere but if you are trying to replicate the authentic Chicago deep-dish style I would use only metal pans. If you use a dark anodized deep-dish pan, such as those sold by pizzatools.com, Chicago Metallic, American Metalcraft and others, you will not experience rusting if that is a particular concern.
I might add that I have been reading about this subject for years, including at forums dedicated to professional pizza operators, and I can't recall a single instance where a commercial deep-dish pizza operator used a non-metal deep-dish pan to make authentic deep-dish pizzas. If authenticity is not a consideration, then you will no doubt be able to bake a deep-dish pizza in a stone or other non-metal deep-dish pan, just as fruit or savory pies are baked in glass or other non-metal pie plates.
Peter