Making a tube rivet

Use dead soft sterling silver tubing that matches the size of the drilled hole, so that the tube just fits into the hole. It needs to be rather snug but not forced.
Using a permanent marker, mark a line where you will cut the tube. Leave about 1/8" or 3mm of silver sticking out on either side of the stone.
Cut using a jeweler's saw. File and sand the ends smooth.