Have multiple applications you want a single project to serve? Here is an example of a single project designed to accommodate two uses.
I had many sources for inspiration including one of the instructables' examples that uses a plastic bin, hose, spring and a quick connector. The first trailer I built went for minimal parts count using a piece of one half inch thick sheet of scrape plywood u-bolted to a seven sixteenths diameter axle and tires from a stroller. The hitch was made from a piece of bicycle tire wrapped around the rear basket handle and bolted onto the top and bottom of the end of a piece of conduit, that was u-bolted to the plywood. (see last picture below)
For the second trailer I also used a one half inch thick piece of plywood (three quarter inch next time) u-bolted to a one half inch axle and tires from a wood carrier cart, and a two inch caster wheel.
My original plan was to bolt the conduit to the metal frame running perpendicular to the axle (see first picture of last step) but I decided that I wanted only the trailer axle to carry 95% of the load. Put another way... I decided not to build a semi-trailer where a large portion of the load is carried by the rear tire of the bicycle. I used the half-inch plywood (new) to start with because it was handy, only needed a trim and was light.
The u-bolt arrangement permits the plywood to be leveled without bending the conduit permanently. The first piece I used had enough contact area together with a slight offset angle to keep it from slipping when the u-bolts were tight. I put a carriage bolt through the second piece of conduit (which had a straight end to fit through the PVC pipe) because it was too short to provide enough contact area with the plywood. Even though attached in a small area I expect the conduit will bend before the plywood will break, especially when I replace it with three quarter inch sheet. If the conduit bends or the plywood breaks from too much weight then I have not done my job in balancing or securing the load.
Step 1: Two Out of Three Ain't Bad...
I try to avoid using the dropout with any carrier/trailer project since wheel realignment can sometimes be a pain. Instead I use the fender mount bolt holes above the dropout to keep axle and carrier adjustments and maintenance separate.
In most cases even If I use the dropout hole an adapter is required to match the frame bolt holes with the holes needed for the carrier. In this trailer project I decided to use a 2 inch diameter caster wheel to keep the cost very low since I found a good one at the flea market for a dollar and a caster wheel provides two of the three required axis of rotation.
To mount the caster wheel to the frame I thought I would need to make an adapter but then the idea hit me that all I really needed was to cut parallel flats on the caster wheel and drill holes to match the fender mounts.
This initial design resulted in a hitch design that worked only if I did not stray from level ground, rest the bike on the kick stand or let it fall over. It soon dawned on me that a good trailer hitch design required provision for all three axis consisting of yaw, pitch and roll. Since I live in a hilly area with many bumps, gulleys and inclines this setup, which lacks roll, was not good enough to get me past the driveway so I started thinking about a way to add roll at very low cost..