Cut two 10-1/2x8-inch rectangles and one 6-1/2-inch-diameter circle from each fat quarter. Join the short ends of one pair of matching rectangles, stopping each seam 1 inch from the same (top) edge, to make a tube. Sew a matching circle to the tube's bottom edge to make a bag. Join the short ends of the two remaining rectangles, leaving a 3-inch opening in one seam. Sew the matching circle to the tube to make the lining.
Turn the bag right side out. Insert the bag into the lining with right sides together. Sew around the upper edges with a 1/4-inch seam allowance, then turn right side out through the opening in the lining. Sew the opening closed. Press the top edge and sew 3/4 inch and 1-3/4 inches from the edge to make a casing. Starting from opposite sides, thread two 1-yard pieces of 3/16-inch-diameter cotton cording through the casing; knot the ends of each cord and pull to gather the fabric.