We are turners here. You have to be more creative than that. Turn a rod and cutting is way too simple. Finding a rod and just cutting it up is not even a challenge. Just go buy a couple sets and paint the pieces then. Turn a red rod and drill it out for a center black rod and then reverse the colors. Then do something fancy in the center and then part each one off with a parting tool and keep doing the same decoration.
Step it up some

Show us some turning. Creative minds.
Sounds good John,....I was thinking that after you turn, decorate and part off that you mount the checker in a wood block and turn the backside as well....just like turning a pendant disc....both sides turned....after all, we do have lathes and need an excuse to turn more!
One could turn some separate "Kings" that are different from the regular checkers....maybe double thick in each color.
I would turn some extras in case one gets lost.