Well, I am no genius, nor am I very good at giving descriptions of mechanical systems, but I'll try my best.
You have a double din sized opening. Be carefull, because some of the double din openings (like the one on my Focus) isn't large enough for the screen to fit without using a dremel to either the screen case, or the radio opening.
What you are going to want is a pin & slot type system. The camera rests in a housing that is mounted to a bracket that has two pins sticking out the sides. These pins stick into a divot/hole made in the plastic (of the car) on the left & right sides of the screen. The screen is allowed to swing on the pins freely, so I would recommend putting a lip on the front of plastic to allow the screen to move down a little bit. To put it up, just give it a push up and back. That should work as long as your Civic has as much room behind the radio opening as a friend of mine's '93 Civic.
Hope this atleast helped brighten your own ideas.