I do make my own sauce, but you can certainly keep it easy and buy prepared sauce. I also make my own dough, which I'll be providing a recipe for here. But, you can purchase a store bought dough and use it just as easily. The trick is lightly oiling your grates, really cranking the grill to get things started and making sure to oil up the dough. I also think making "personal" size pizzas keeps things manageable and moving right along.
Typically, I will make the dough the night before and let it rise in the fridge so it's ready to go when I am. (I do let it come to room temp for about 45 minutes to an hour before handling).
This is the recipe that I've found so far to work best:
Grilled Pizza Dough
Gourmet June 2003
Chris Bianco, the owner of Pizzeria Bianco, in Phoenix, makes our favorite pizza dough. He showed us his technique for our October 1999 issue, and we've been building on it ever since. Here, we've adapted his recipe slightly to make it work on the grill. This recipe is an accompaniment for Grilled Pizza Margherita.
Makes 1 lb dough, enough for 2 (9-inch) pizzas. (I make 4 from this)
1 (1/4-oz) package active dry yeast (2 1/4 teaspoons)
1 3/4 to 2 cups unbleached all-purpose flour plus additional for kneading and dredging
3/4 cup warm water (105-115°F)
1 1/2 teaspoons salt
1/2 tablespoon olive oil
Stir together yeast, 1 tablespoon flour, and 1/4 cup warm water in a measuring cup and let stand until mixture appears creamy on surface, about 5 minutes. (If it doesn't, discard and start over with new yeast.) Stir together 1 1/4 cups flour and salt in a large bowl, then add yeast mixture, oil, and remaining 1/2 cup warm water and stir until smooth. Stir in enough of remaining flour (1/4 to 1/2 cup) for dough to come away from side of bowl.
Knead dough on a work surface with floured hands, reflouring work surface and hands when dough becomes too sticky, until dough is smooth, soft, and elastic, about 8 minutes. Divide dough in half and form into 2 balls(I did 4-- 2 a piece inside of oiled gallon zip top baggies), then generously dust balls all over with flour and put each in a medium bowl. Cover bowls with plastic wrap and let dough rise until doubled in bulk, about 1 1/4 hours. Dough can be allowed to rise, covered and chilled, 1 day. Bring to room temperature before kneading.
Form pizza rounds:
Do not punch down dough. Gently dredge 1 ball of dough in a bowl of flour to coat, then transfer to a lightly floured work surface. Holding 1 edge of floured dough in the air with both hands and letting bottom touch work surface, carefully move hands around edge of dough (like turning a steering wheel), allowing weight of dough to stretch round to roughly 7 inches in diameter.
Lay dough round flat on floured surface and continue to stretch by pressing dough with your fingertips, working from center outward to edge, stretching it into a 9-inch round. Transfer to a large floured tray and make another round in same manner, then place it next to other round. Lightly rub a long sheet of plastic wrap with flour, then invert loosely over pizza rounds and let them stand to puff slightly while preparing grill, 10 to 20 minutes.
To prepare gas grill:
Preheat burners on high, covered, 10 minutes, then reduce heat to moderate.
To grill pizzas:
Remove plastic wrap from both rounds of dough and lightly brush dough with some oil. Carefully flip dough rounds, oiled sides down, with your hands onto middle of lightly oiled grill rack and brush top of each with oil. Grill crusts, uncovered, until undersides are golden brown (rotate them if 1 side of grill is hotter than the other), 2 to 3 minutes on gas grill or 4 to 6 minutes on charcoal grill.
Flip crusts over with tongs and a spatula and top each crust with half of tomato sauce, spreading evenly over dough and leaving a 1/2-inch border around edge. Sprinkle mozzarella evenly over sauce and grill pizzas, covered with grill lid, until undersides are golden brown and cheese is melted, about 3 minutes on gas grill or 5 minutes on charcoal grill.
Scatter basil over pizzas. (If using meat-- place pre-cooked meat on pizza after sauce and then cover w/cheese).