How do you keep a rug on top of carpet from moving?

The only think that might work is a grippy latex rug pad, but it still might slip a little,

I have used the Rubbermaid drawer liner rubber stuff and mine stayed put

http://homeguides.sfgate.com/stop-area-rug-slipping-carpet-72633.html

have you tried the waffle back cushion they use for area rugs that should work. Available on Amazon, and Home depot in the flooring dept.

I would use actual backing that they put under wall to wall slightly smaller then carpet, doesn’t budge.

You can buy anti-skid pads for under them.Most home improvement centers that sell rugs should have them.

The anti skid pads are very effective, can get them at craft stores and Home Improvement centers, they come in a variety of sizes.

For a rug on a rug, you need a blanket cloth/felt type material in between. The anti slip mats are meant for use on hard surfaces only. If you can't find one at a large box store, Ikea also sells their own brand called "stopp filt". Buy one as close to the rug size as possible and trim if necessary. The main problem is the base rug isn't firm enough to fully support the rug on top.