Ford Fusion has banging noise in right rear area.

Since it is front wheel drive that eliminates a few things. I is highly difficult to find some of these because sitting there is constant pressure on most of them. When they go airbourne so to speak things no longer have the pressure and they can make the noise as they settle back in to place. You have stated two obvious ones. There could be a stabilizer bar that is loose or a coil spring that is broken.

You might try jacking the car up and seeing if you can find anything loose under the car. Be careful!