A few years ago we were at Lowe's looking for tile for our fireplace surround and hearth remodel, and I loved the 4x4 slate. It looked like the perfect size for coasters, and it was only $5.49 for 9! So we bought them, I cleaned them with soap and water, and I added some cork board to the back so they wouldn't scratch my furniture. You could just as easily use those adhesive felt circles.So, so very easy. The only thing you need to know is to buy the special glue for stone to attach the cork, and let them dry for at least 24 hours before you use them. The vapor from the glue will damage your furniture if it is not completely dry. (Thankfully I read that somewhere and didn't learn the hard way!)
Let me know if you take on this project, and please share pictures!