Pack-Right offers car clips or J hook accessory straps. If you don't have a luggage rack open your car doors and look for a ledge along the roof line.
The J part of the hook is about as big as the end of your finger. Most (not all) vehicles have a ledge. Some times it's a rain gutter or maybe under the weather molding.
When you tighten the straps over the car top carrier bag, the tension pulls the carrier against the roof and pulls the clips up and holds them in place. The carrier bag must be packed full and tight so gear doesn't shift and loosen the straps.
Pack-Right also offers a roof protection pad which is a good idea for this application. The pad also offers traction on the roof to help hold your gear in place.
Always test this set up before you hit the road. Every stop check the clips and straps to be sure they are tight.