Most laptops have a spring-loaded mechanism that "pops" the tray out when you hit eject. The double-decker CD situation you have going on may simply have wedged the tray so that the spring just doesn't have enough force to move it.
From here, advice gets dicey because it's more of a "feel" thing. You should be able to apply a small amount of pressure to "help" the internal spring overcome the resistance. The problem is there is a point where too much pressure will break stuff.
I'm at a loss for how to describe how much force is too much, but you need a little pressure (pulling the tray out) at the moment the eject button is pressed to ensure it "releases" and then you may need more continuous pressure to overcome the wedge the two discs have created.