I have had these plain cork coaster for some time now. And have have HUGE bags of scrap fabric I can't throw away. I know they look a little messy, but that was kind of the look I was going for.
You will need some scrap fabric or any fabric you would like to cover your coaster with. This part may not be good for your machine, but it worked fine with mine, since the coasters are thin enough, I just used a needle for thick fabric, like a leather sewing needle or a denim needle.
After sewing on all the fabric I turned it over and trimmed all the fabric then I sewed all around it one more time. You can always sew some fabric on the bottom or a nice piece of felt.