I was having the same issues with my explorer. If you remove the passenger side rear panel you will find the factory subwoofer box.
Now the box has a 8'' woofer in it.
You can easily mount a shallow mount 8'' in the factory box and it will give you a great sound. I dont know how loud you want it, but this is a great low cost option that doesnt require a lot of modification. All you really have to do is run cables, add some polyfil to the box and mount the sub.
On my Explorer this is what I did to fit a 10'' JL 10w1. When you remove the box, you will see a cavity built into the body of the truck, on the bottom of that hole I cut off about 3 inches to increase the size. I then applied a nice layer of dynamat to help with sound.
For the actual enclosure I cut a whole in the back and used fiber glass to extend the box into the cavity I was telling you about. This extension is what gives you the room to fit a larger sub. After that I made a few measurements and cut the original opening to fit the sub. I added a 10'' speaker ring and fiberglassed that in with a few supports.
The sub sits behind the factory panel and you could never tell it was even there. Now this box is not ideal for sound quality, but unless you are an audiophile you will like the increase in bass.