Baking pizza without an oven
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.