Any aftermarket products that do not come with the seat from its manufacturer are not advisable. They may void the manufacturer's warranty.
Additionally, if it's not been crash tested, it could be a problem in a crash. It sounds like a high risk for projectiles. Remember that anything not fully secured inside the vehicle's cabin will continue to travel at the speed the car was traveling right before impact. Think about the tray you'd like to design and imagine it traveling at 30 mph (or faster) towards the occupants of the car....there is a great risk of injury.
To summarize, articles not fully secured can be projectiles in a crash...and articles fully secured to a child restraint could void the warranty at best and--at worst--possibly cause the restraint to malfunction in a crash.