Mark,
I have only done this once, so I cannot speak for anyone else who has done it a number of times.
My issues were managing hot spots on the grill. I cooked the hell out of one half of the dough, while the other side remained raw. So distribue your coals evenly according to their heat (Duh, right?). I plan on using a vegetable grill tool to start the initial side of the dough, so I can move it around easily and also pick up the dough as a whole to see where its done and not done.
The main thing TravelingJ told me was to cook the toppings first, as they will not cook on the pizza. So prepare that in advance. I threw the dough on the grill first, and let it get golden brown. Then flipped it and topped it with toppings. At this point you need to monitor the bottom, as it will cook quickly, and is easy to burn. I finished mine off in an oven (low heat) so the mozzarella could melt. This also keeps it warm while I cooked the other pizza(s).
There are half a million dough recipes on the internet, but this one was given to me. Providing TravelingJ doesnt care, Ill type it up and post it. It was delicious. It was more of a thin crust than it was a thick.
From what all I have read on the internet, this can be done with a gas grill. But then you also miss out on the smoky flavor of the charcoal. To each his own. But there are plenty of debates on Gas vs. Charcoal (im sure you have all heard of them).
Once I have approval from TJ, ill get the recipe out tonight and type it up (providing he is cool with it).
This was fun for the whole family, so be prepared to do this alone, or invite someone to jump in. You may want to give it a try first, before you decide to do this for your next home party or something though. Like I said, I burnt the bottoms of these pretty good. I will not do it again though! (probably will, but I have to try).
-Chrisso