Some good ideas above.
But rather than a beach ball, which is far too small, you'll need cover pillows. These are about 10' long and 4' wide and inflate like giant beach balls, floating on the water and supporting the cover. My late dad used to get hold of used truck tire inner tubes and use about 8 of them tied together and tied to keep them in the center of the pool and cover because they were free and easy to get.