Is there any type throw rug that will not slide on a nylon rug?
they make a non skid pad to solve this problem try one of them, they go under any rug you want to use
Very few rugs are made with a non-skid backing. But a pad to put under the rug is very common, and should solve your problem. Any place you buy a new rug should also be able to sell you a pad to go under it. Just make sure it's a rubbery pad and not just the foam cushion that goes under wall-to-wall carpet.