As much as I love pizza, my real love is grilling. I've grilled pizzas directly on the grill grate, which provides a nice pizza, but in my opinion it is no where near as good as a pizza stone pizza. My goal was to get my high quality indoor oven pizza stone method (the typical 550 preheat with a broiler finish) to also work on a standard Weber charcoal kettle. I got a pizza stone from Red Sky Grilling and the first few times I used it I failed miserably. The stone was hotter than the dome temperature, which burnt the bottom of the pizza and left unmelted cheese and raw dough on top. I'm aware that this doesn't happen on Green Eggs and other grills that have that ceramic heat retention ability. This issue might also not happen if you have a real small pizza stone. The problem I was having was that not enough heat was coming up around the stone to heat the dome of the grill. This problem is common when you only place coals directly under the stone, or when you have a HUGE pizza stone.
Anyway, I think my solution is unique and I wanted to post it here, in case anyone else was having this problem as well.
My solution is to put a fully charcoal basket on top of the grill grate, next to the pizza stone. A little bit of charcoal under the pizza stone is enough to get the stone hot enough for a great pizza, and the charcoal basket sitting on top of the grate is enough to heat the top of the pizza. This is similar to a brick oven pizza where the flame source is sitting next to the pizza pie.
It worked perfectly.
More exact details are posted over at my Grilling Blog: http://grilling24x7.com/stone.shtml
Let me know if anyone has any questions or ideas.