Here's a sketch I made for a rigid mount one wheel trailer. It would be a bit
akward if it were longer than three feet long or so. In this sketch I haven't provided for a hinged spring suspension, but that would be considered if I were to build this.

Ohio allows the motorized bicycle to have three wheels and one rider. The side car makes the most sense of one wheel, but again Ohio says you have to stay within three feet of the edge of the road when operating the motorized bicycle.
So the rigid mount one wheel trailer would make sense here in "The Buckeye State".



By using the front end of a discarded kiddie bicycle with a small wheel the "rake" angle could set the caster of the wheel to follow the turns like a "dolly wheel", much like on the front of a grocery shopping cart and while still providing support to the weight of the load in the trailer. In ohio the trailer would easily fit into the "three feet zone" of the edge of the road and be compliant with the law.

The mounting of the trailer shows two upright tabs that fit over the axle of the rear wheel and be tightened down. At the extended end of the trailer mounts toward the pedal cranks are a pair of hooked plates that attach over the top of the lower frame. Thus with the rear dolly wheel's leverage on the bicycle frame the axle would serve as a fulcum and the clips which hold over top of the lower bike frame would render the mounting solid and stable.

Operating this type of trailer would take some getting used to in tight spaces as it would have a wider sweep than the trailer which hinges at the back of the bicycle on a ball hitch. But in many cases when out on the open road there's plenty of room.

In the sketch you can see there would be room under the trailer's box too. Perhaps a smaller box that would contain a pull out drawer and provide adeqate road clearance could be built there.