Diamond disks can be stored by sticking them on the flat side of a refrigerator and/or metal filing cabinet (dry the magnet side first).
If these surfaces are flat and clean they serve well as safe storage. You might want to let them hang off the edge about a quarter of an inch so you can pull them off. We also recommend gluing two small wooden or plastic blocks on the refrigerator to serve as a lower support to minimize the chance of dropping the disk.
The magnetic pull is quite strong but be careful not to drop them on the floor on their edge as they are not indestructible! If this should happen the edge will no longer be flat. The disk may be trimmed to remove the bad area but it's something that is much easier avoided than corrected.
In our shop we actually use one the excellent Magnetic Disk Organizer. We highly recommend them.