I think the 2007 Chevrolet Cobalt 2 door's roof is just too short to safely carry long items like kayaks. You normally need a base rack system that will have sufficient distance between the front and rear base rack crossbars to provide a solid platform to safely carry the kayak. Thule Racks and Yakima Racks do offer stretch kits for many short roof lined vehicles that will spread the front and rear crossbar distance out but some reason they haven't been able to engineer the stretch kits to work on your car.
I don't know if these other options will work, but I've seen many people try out these pretty cheap solutions when a Thule Rack or Yakima Rack base system won't work...
the first option is a
foam blocks kayak kit and the second option is the
inflatable roof rack system. If you do try these out you definitely want to use bow and stern tie-down straps to fully secure the front and rear of the boat when transporting it.