Try Walmart for fitted playpen sheets - they're 2 for $10. And Babies R Us has a ton to select from as well.

Parents must provide me with the playpen, 2 fitted playpen sheets, a blanket & stuffy/soos, or if they're on a cot, a mattress protector (crib size works for my cots), 2 sheets, pillow, blanket & stuffy. If they don't provide these items on the first day of care, they're not to stay over for nap.
I ask for 2 sheets just incase of a kid getting sick, or that baby that's super drooly! I wash the sheets every 2nd week.

Put it this way, how would you like it to sleep on one of those vinyl sleep mats without a sheet over them!? NO THANKS!