If you can live without a food-safe certification
Quarry Tiles can be used in place of a Pizza Stone.
At about 25 to 40 cents each, it can be a cheap experiment
Look for Natural Red Clay (lead free) tiles. High-fired tiles do not crack as readily as low-fired tiles.
Baking Stones (& Quarry Tiles) should not be exposed to direct flame, so make certain your Bar-B-Q has a flame diverter before using them.
All stones absorb some moisture, so pre-dry (temper) the new stone prior to first baking use. A slow gradual temperature increase will dry the stone gradually, preventing cracks.