Easiest is to install it on the coop wall rather than the run wall. There, you can just cut a rectangle out and use that wall piece for a door. If you cut the side you want to hinge first, you can install the hinges before finishing the cutout and it will be perfectly aligned. Then you just need a way to latch it that's beyond a raccoon's abilities. I have a hasp that twists on the chick coop; super easy for a person, impossible for a raccoon even without a lock on it.
Or, you can be really fancy and buy an automatic door kit so you can open/close it on a schedule or with a remote control or on a light sensor...
