Revised my original disk box design to allow for displaying the disks right side up.

The top contains tabs to click into the square hole in the upper right corner of a disk. These may be a little tight but are intended to catch the disks so that you can pick the box up without it falling apart. If it seems too tight a little sanding with an emery board should do the trick.

The bottom has small button tabs in the corners to catch the circular recesses at the bottom of each disk. These do not catch as much and likely will not need to be sanded.

I'd recommend putting the top down on a table and insert the top of each disk first, then place that into the bottom, pressing down on each corner.