A semi-permanent suggestion, but U nails maybe?

Have you tried putting the hook side of velcro on the bottom of your rugs? That should grab onto the carpet underneath.

I haven't tried this, but I was thinking of using a carpet stapler with carpet staples to staple the rug down into the carpet. I am renting also and want to get some rugs to put over the carpet. Hope this helps!

There's a kind of sticky pad that you can use. I'm not sure whether or not it leaves a residue, but it's the only thing I've found to work. It's just tacky enough to keep the rug from moving around, without being as permanent and hole-creating as staples or nails. It looks like this: http://www.google.com/products/catalog?q=rug+pad%2Brug+to+carpet&hl=en&client=firefox-a&hs=KVR&rls=org.mozilla:en-US:official&prmd=imvns&bav=on.2,or.r_gc.r_pw.,cf.osb&biw=1137&bih=651&um=1&ie=UTF-8&tbm=shop&cid=14753576235045923528&sa=X&ei=VhazTvzDFpHViALSpJVH&ved=0CKcBEPMCMAQ

We got one at a rug store.

I always use the rubber perforated shelf liner (the kind used to protect your glassware in the kitchen) that you can buy in a big roll. You only need a little bit. Just slip it under the occasional rug. It's got great traction and is very inexpensive to use.

http://www.linensource.com/jump.jsp?itemID=2473&itemType=PRODUCT&path=1%2C2%2C10%2C43%2C60&iProductID=2473&color_id=&size_id=&price_id=&sequence=null

Try a rug pad it is a thin felt like material that is slightly tacky. Works like a charm!

I would just use slender brads with flat heads and tack down the corners directly into the wood through the carpet. The holes will be tiny and easily filled if the carpet is ever removed. Just do it in the corners - it should be enough.

I have area rugs on carpet (ick, can't wait for hardwood floors) throughout my home. The sticky pads mentioned above, available at home improvement shops and rug stores, work well and in my experience do NOT leave a residue on the carpet underneath. They're pretty much a 1-use item though and so they don't always work once you pick it up and try to move it (to a new room/new home). Live with the carpet where it is for awhile, make sure that's where you want it, then apply the tacky pad.

Perhaps you could do what Martha suggests and apply lines of acrylic-latex caulk on the bottom of the rug every few inches to give the bottom of the rug some grip.

http://www.marthastewart.com/272310/slip-proofing

I also vote velcro! Good luck!

Your rug is woven the carpet is woven, right? Why not stitch the corners and a few points along the edge with a Speedy Stitcher $10 from Campmor. Its easy enough just cut when its time to move or clean and the rug WON"T MOVE.