If you go the IR route, you really only need two interrupters. You would just sense the direction of movement into and out of the box. Increment and decrement your count based on that.
As you described it, there is only one entry and exit point to the box.
My initial thought was more along the lines of Peter's and it sounds like the most fun and interesting, but probably the most complicated to build. If you did go that route, you could add a flag to the pedestal that gives a visual indication of the number of books as well.