They should always be stored upright in order for the internal safety/relief mechanism to work.
" Propane cylinders should always be positioned so that their relief valve is in direct communication with the vapor space of the container. Cylinders that are stored vertically upright will have the relief valve communicating with vapor space. Regarding the cylinder relief valve, it is important to keep the safety relief valve pointed away from anything that escaping propane could come in contact with possibly causing a fire or accident. If cylinders are stored improperly, such as on their side with the relief valve in contact with propane liquid and the safety relief valve opens for any reason, liquid will be escaping instead of vapor posing a much greater danger. In short, be sure the relief valve is communicating with the vapor space of the tank. All consumer propane cylinders should be stored vertically upright in all circumstances."
Propane Cylinder Storage - Safely Storing LP Gas Bottles