Roofing choice for outdoor sandbox cover
Purchase a 4'x8' sheet of southern yellow pine (SYP) plywood that's been pressure treated for ground contact applications.

Typically that's an ACQ treatment at 0.40 or 0.60 pounds per cubic foot, and SYP because that species of wood accepts and retains treatment extremely well. 

"Ground contact" is the highest level of treatment, and I chose it over the lesser "above ground" treatment because it is directly exposed to the elements, and the additional cost should be negligible for just 1 sheet. 

You wouldn't even have to paint it, but if you do, use a paint designed/intended for use on treated decks. 

The only thing I'd be concerned about is a finding a way to prevent the sheet of plywood from flying away during storms and periods of high wind gusts.

Depending on the thickness you purchase, it will begin to warp as the main failure mode, not decay or rot. To prevent that you may want to build a frame for it by screwing treated SYP 2x4s on the bottom around the perimeter, and maybe one or two running down the middle of it. Make sure the screws are short enough so they don't stick through the other side and poke little fingers when removing the sheet to play.