I’ve not done it on a propane grill, but several times on a charcoal grill. It’s become our new favorite pizza.
We usually make our dough, but I don’t see why the canned wouldn’t work.
We don’t use a stone or a peel; expect some very hot hands with this method. (Personally, I don’t see the point of grilling pizza if you’re going to use a stone - just stick it in the oven already. I do have a pizza stone, just don’t use it on the grill.) Some tongs and/or a very large spatula will help.
Roll out pizza dough per instructions. Best to stay fairly small - 6-7" diameter max. Think personal pizzas rather than family pizza.
Fire up the grill. While it’s heating get all your toppings ready, you’ll need them handy at the grill. When the grill is hot, turn half of it down for medium-heat cooking and leave half at fairly high heat.
Brush one side of dough with olive oil and place that side down on the grill over fairly high heat. Cook for a few minutes (3-5, maybe?) until the crust gets lovely brown and toasty. If you try to move it and it starts to stick or tear, it’s not done yet. You’ll have a few dark brown spots, if you’ve got too many turn the heat down a bit.
Brush the other side of the dough with oil and flip it over on to the lower-heat side of the grill. Add your toppings - not many - and cook until the toppings are melty-warm and the bottom is brown and crispy. Adjust heat down if bottom burns before toppings are warm, or up if it doesn’t seem to be getting done.
We usually top with a touch more olive oil, garlic, chopped tomatoes, chopped fresh basil, minced red onion, and a little mozzerella cheese. Yum!
If you’re doing meat toppings, you’d want to cook them first if that’s needed. If you want cooked veggies (as opposed to hot but still crispy veggies), saute them first also. This method won’t get hot enough to really cook the toppings, just hots them up.
Go light on the toppings - it’s easy to overwhelm the pizza, and the toppings won’t get hot and yummy.
Serve IMMEDIATELY if possible. While these are still good after sitting a bit, they’re far better when served straight off the grill. (If you have to hold them for a while, try popping them back on the grill to reheat and crisp up again, or run them through a toaster oven.)