Last year I made 4-inch coasters using various quilt block patterns. I free motion quilted the tops using a low-loft batting (1/16 inch Thermore brand that I bought at Hobby Lobby). After quilting, I layered the quilted top, a piece of flannel-backed tablecloth plastic and a plain back square together.
I sewed a 1/4 inch seam around the edge, leaving it open at the center of one side so I could turn it right side out. The corners looked better when I stitched one or two diagonal stitches at the corner instead of a sharp turn. (I use an enameled chop stick to push out the corners.) After turning it right side out, I top stitched around the outer edge and did not have to hand stitch the opening.
The plastic protects the table tops. I used up some old tablecloth scraps and then bought more at Hobby Lobby. (Some I looked at was too thick.) I tried a piece of a plastic tablecloth that wasn't flannel-backed, but it doesn't stay in place as nicely as the flannel-backed.