Turn the coasters to the right sides out. Push out the corners with a chopstick to make the corners square. Also, turn the open edge in 1/4", putting one side over the batting. Press.
Sew, starting with the open edge, less than a 1/4" away from the edge, around all four sides. Be sure to sew a straight line and back stitch when you start. When you get to the corner, stop with the needle down and turn the piece to make a sharp corner stitch.
Before you get to the end of the final side, stop 1/4" away from next side stitching. Turn the corner and sew around the square lining up the edge of the stitching to the edge of the sewing maching foot. (This is usually 1/4" away).