I have been using the same piece of EPDM roofing for over 15 years in the floor of my tent. Go to a commercial roofing company or a building supply house that sells to roofing contractors. Ask to buy a piece of .045 EPDM. Should cost you about $50 per 10' X 10' piece. Better yet, if you know any roofers ask them if they have any scraps. Since EPDM comes in rolls up to 40' X 100' a scrap can be pretty big. The EPDM that I got was tearoff from an older roof. I had to scrub the mud off it but it was free. You can cut it to size with Fiskars scissors. If you punch a hole in it, you can repair it with a tire patch.
EPDM is black and totally waterproof. There are also white TPO roofs out there but they come in more narrow sheets and the seams would have to be heat welded with a special machine before you could use it.
Many Klatch