Where can i get outdoor heating suitable for a childs playhouse?

I would be reluctant to use anything other than electric heat in that situation. They make an oil filled space heater that looks like an old fashioned radiator. That might be a good choice. Another option is to light the house with halogen lights with the proper guards in place to avoid burns from touching the hot surfaces of the lenses. Halogen lights give off a lot of heat, which may enough, depending on how you plan to use it and what the temperatures outside are.

Avoid anything inside the playhouse that burns any kind of fuel, as carbon monoxide poisoning is always a concern with combustion

Look for a local HVAC company and talk to the professionals. You sure don’t want to make a mistake .