I was originally planning on making the checkers out of plastic lids or getting little wooden circles to paint, but then I found some little round wooden game pieces as part of a tic-tac-toe game in the $1 section of Target. You could also use mini-erasers, candies, and miscellaneous other objects instead of checkers.
I added a little tin (also from the $1 section) to put the game pieces in. The duct tape mat is really durable and can be wiped off. It can be rolled up of folded for easy storage. I really love how this little homemade game turned out, and I can't wait to begin playing checkers with my kiddos!