I'm not a table mechanic, but I've done a fair amount of fabric repair on old guitar amps and cases. I would be very reluctant to put a single drop of super glue on cloth. It wicks into the fabric like crazy (hell, it is called "crazy glue", right?), and sets up very hard. Plus, you will have to remove it from the slate when you recover the bed.
What I found was most effective is to get some Elmer's glue and paint a thin layer of glue on the surface of the wood (in this case, the slate) with an artist's paintbrush, and let it dry a minute or so until it is tacky. Then just push the cloth back down and burnish it with a smooth piece of plastic until it stays down by itself. You can actually work the stray fibers into the cloth with a pin, and if you don't use too much glue you will have a very unnoticeable repair.
Craft stores sell a special glue for this purpose. It is called "Tacky Glue", or something like that. I believe it is just very thick Elmer's, so I use what I have on hand and let it thicken by drying a bit after it is applied.