Support: Support the drive internally by using two right-angle shelf-mounting wall brackets (screw them into the back of the door), and two flat metal right-angle brackets (to allow you to screw it into both the shelf bracket and the side of the DVD drive). Ask for these at your local hardware store.
this is a great idea., i think ill include this in my cab.
Thinking about this after a sleep, I feel more inclined to recommend a metal cage to house the DVD drive.
The best place to find a DVD-sized metal frame is from an old computer - fortunately old CD housings will do just fine. If you don't have one lying around, someone probably does. Or find out who recycles computers near you.
Bolting the whole cage to the wood makes it much more secure than simply screwing brackets into the back. On the one I built (yellow cab), you could apply quite a lot of pressure to the DVD cage very safely. This is because everything was supported by 4 x 1/4 inch bolts secured through the door. As you only have to undo 4 bolts, you can pull everything off very easily if you need to.
I literally have a metal DVD cage just like that one lying in a pile of junk behind my house. You are welcome to it, but someone near you must have one too!