Placing a pizza stone directly on a burner will likely lead to cracking. If you are limited to stove-top cooking, there are two routes that you might use to make pizza.
First option, steal some of the techniques used for making grilled pizza:
- Preheat a large skillet medium-high with its lid in place.
- Cook the crust on one side, flip it over, then place the toppings while the second side cooks.
- Cover the pizza after it has been topped.
Second option, use (or improvise) a dutch oven:
- Preheat a large cast iron skillet or dutch oven over medium-high either with its lid
in place, or heat the lid on a separate burner.
- Stretch the dough inside a pie tin and up it's sides.
- Top with sauce, cheese, pepperoni, etc.
- Place 4 wads of aluminum foil in dutch oven to raise pie
tin off bottom.
- Set pizza in dutch oven and cook.
In either case you will be limited to making fairly small pizzas.
Keep your crust relatively thin. A thick crust is going to burn before it is fully cooked inside. It may also be beneficial to pre-cook as many of your toppings as possible prior to placing them on the pizza.