just get an electric stapler ($20 at a hardware store).. cut the corners at a 45 deg angle, fold and staple the tabletops... they will be semi-permanent, no laundry bills, wipe off easily and no sliding.
Turn table upside down on another table, with vinyl facing up.
Go to the center of the first side, staple 3 staples, 1 in the center and 1 an inch away from the center on each side.
Go the OPPOSITE side and repeat, pulling firmly but not excessively, DO NOT go round the table, go to OPPOSITE side.
Go to the 3rd side and repeat first side.
Go to the OPPOSITE side and repeat second side.
Trim away extra corner fabric, leaving approx 1 inch.
Fold up the corner right in the middle, staple in center.
Fold each side of the corner up, one at a time, and staple, each time smoothly pushing the extra fabric up and over, folding as nicely as you can.
Repeat for each corner.
Now go to each unstapled quarter and divide in the middle, staple and repeat, always going to the center of each area, over and over. Each area will get smaller and smaller but any slack will disappear this way.
Repeat for each unstapled quarter.
Now trim away any extra fabric outside the staples to keep them from being irritating.
Do not use bleach in the water, but simple green will clean completely without damaging the vinyl. Do not be tempted to do this with a hand operated stapler. It will take twice as long, your hand will hurt and when you have to replace the vinyl in a year, you will go get the electric one anyway. Be sure to read the package well, most electric staplers take heavy duty staples and you will need to be sure you get the right ones. they should be available at the same store. the lighter duty staples will jam and make you say naughty words.