Double sided tape works great. Carpet on carpet isn't a great idea but doable. You can find double sided tape at hardware stores and put it on the back where one side sticks to the rug and the other side sticks to the carpet. Velcro also works great but you'd have to "screw down" the velcro to the floor and tack the top part to the rug. Try double sided tape and if nothing else, duct tape is the answer. Ugly but it works.

you can always put heavy furniture on the edges of the rug to keep it down.