first i would mount the sliding surface of the box. make sure you leave enough space to the side of the sliding surface, probably 3/4 the distance of the diameter of the coping, so that you can attach the coping. i would probably do this buy pre-drilling some angled holes into the coping so you can attach it with screws to the frame.
the thickness of the sliding surface should probably be about 2/3 to 3/4 of the diameter of the coping so that when you hit it you will be sliding smoothly on both your surface and the coping.