Diamonds are considered Trade Commodities and are not allowed in your OCD. Other common illegal items are RP Containers, T3 Autominers, Epic Armors, and Epic Drills. Check out here for more information about the Orbital Cargo Drone, and here for the various Trade Commodities.
Diamonds are used for crafting Carbon Blocks, and those blocks can be stored in your Orbital Cargo Drone. They are considered Epic items when considering their OCD Stack Size, similar to Xeno Blocks and Autominer Cores.