Can a flat and level roof be waterproof?
EPDM rubber roofing might work for you. It can be installed without any heat or fancy tools; I'm planning to use it for my flat-roofed concreted detached garage. It should withstand ponding water, and because your project is small and your playhouse probably doesn't have plumbing, you should be able to avoid seams, complex flashing, and pipe penetrations. You can install the rubber using an adhesive directly over clean plywood.

It can accommodate a floating deck. I have the book Roofing, Flashing &amp; Waterproofing (For Pros By Pros), which includes a nicely illustrated article on installing EPDM with a floating deck. The method they recommend is to use a non-adhered strip of EPDM underneath the decking sleepers, so that any motion in the decking doesn't stress the roof membrane much. You'll still want some slope in the roof for better drainage, but you can compensate for that in the sleepers, allowing you to have a level walking deck.