We also like to do pizza on a stone on a grill. One thing to remember is put the stone on a cold grill so they warm up together otherwise the pizza stone can crack. Don't ask how I know. Here are a couple of pictures of being lazy and using a Papa Murphy's prepared pizza.
After heating the grill and stone to 550 temperature we throw on some corn meal.
Next slide on the pizza using a peel.
Ready to eat in about 15 minutes.
Grandson said yummy good.