You can sew through clear elastic using a zigzag stitch. Are the tables 60" in diameter? If so, then you need to figure out how much of the fabric will be underneath the table -- say 10"? (This would take the fabric about 5" underneath all the way around.) Then you need to figure out what the circumference is of a circle that is 50" in diameter. I would cut the clear elastic that circumference or a little less. Cut the lycra circle 70" in diameter. Fold the circle into eighths and press or mark so you have divided the edge into 8 equal parts. Fold and mark the elastic in the same way. Pin the elastic to the lycra circle at these 8 places. Stretch the clear elastic as you sew to the edge of the fabric using a zigzag stitch.
That's what I would do. This won't work with anything but clear elastic, though.
Once you have sewn the clear elastic on, if you want to finish the edge a little nicer, you can fold the edge over the elastic and zigzag again so the elastic is covered. This is the way children's swimsuits are often finished.