I'm looking for the exact same thing. The only thing I have found so far are some LED flash lights that project a perfect circle of light with very little scatter. My plan is to mount these in the ceiling probably on one of those adjustable speaker mounts that can be tilted at any angle. I would direct them right into the lap or possibly just forward where a TV tray might be placed for each seat. Of course I would remove the batteries and supply them with 4.5 volt power supplies controlled by "Lightning switches".
http://www.lightningswitch.com/ These are remote controls that do not require batteries in the remotes. The act of pressing the button generates a static charge that powers the transmitter. I already bought one of the 12 volt version for testing and it works pretty well. Rarely does it fail on the first click and require a second click. Based on Mike C's photos of the Berkline chairs in his thread for removing a chair arm I believe it should be possible to mount the lightning switch remote in the seats.
If I could find a better option for the light itself that would be great. It should be possible to buy the optics and LED light sources to build something but it may not be the best option since the LED flash lights are only about $30. Unfortunately I am out of the country right now and can not provide you with the model of the LED flash light. Look at some of these lights, some you can see a reflector and see the LED inside. Others you see only a big round bulging lens. These with the bulging lens are the ones that work. I picked up some of these cheap in Taiwan but they had more scatter and a blueish ring around the perimeter. The original came from Fry's and it makes a perfect circle of light with virtually no scatter or color shift. With this ceiling mounted directed at your lap or TV tray I doubt the person sitting behind you would even know it's on. It puts light only in that circle!
So, that's what I'm planning to do in my theatre as I also will have total darkness with no windows in the room. I did a lot of google searching for spot lights and things along the lines of this...
http://www.activemusician.com/item--MC.3P5Q was the closest thing I could find to what I wanted and it is way too big, way too bright, and way too expensive! So probably unless we want to buy optics, LED's, and other related hardware, the flash lights are probably the only solution. Depending on your ceiling height it might be too close causing the circle to be too small in which case one lens might need to be added to expand it but if you can locate them far enough away it should work fine on it's on.
Keep us posted if you do this. It's going to be some time before I can do mine. My new house/theatre is finally complete but I'm in Malaysia at the moment and can't even move in much less work on this and the million other projects for the theatre.
Monte