I use Weldwood Contact glue to glue on convertible tops and vinyl tops and about everything else in my business. It's more than good enough to hold down a rug. I even glue handle wraps on with it. If it ever needs cleaning off just rub it hard with a rag and mineral spirits. I also glue up quivers and anything else leather with it.Bear in mind, it's a "contact glue". Coat BOTH surfaces, and let them dry, THEN stick them.Depending on the humidity, you'll have as long as an hour open time.Generally, 10 minutes is good.