Recover. Some fabric stores stock the foam backed cloth in a limited selection of colors.
I personally would avoid the online "specialty" suppliers, as their per yard prices are pretty steep. A local trim shop should be able to hook you up if it's a color that's not common in the fabric stores.
Be forewarned, the boards (there are 2 in a wagon) will be very brittle. You can use drywall screen tape and epoxy to reinforce it as needed. Pull the old fabric off, and use either a wire brush or DA sander to remove the old foam crumbles. Contact cement for the fabric and board, and you're done. I have NOT had good luck with some of the aerosol contact adhesives...I use hardware store contact cement and a brush...just have to make sure not to saturate the fabric with it.