It seems as if building an actual
stage floor may be your best option here. However, there are several options you have, depending on how you use the
stage, and your budget. The simplest solution would probably be to
lay a layer of plywood and
cover that with
masonite, at a slight offset, and screw it all together. If you think you may want to screw into the floor in the future, though, or you want to include
stage boxes, you would need to
build the floor up a
bit. There are quite a few threads on here that explain this process.
From a design standpoint, you of course have many other options if the school is less concerned about it being a standard
theatre space. Black vinyl tiles are available that would likely match all the other tiles in the school, and it is possible to find black stained hardwood flooring that could be used. If, and ONLY if, you were EXTREMELY limited in budget, you may be able to remove the tile and simply paint the concrete floor black.