Depending on your trailer and what the tow bike is there are connection points that clamp on to the rear triangle. I have an older burley flatbed that has the rear triangle clamp setup. It has been great for me for 15 years modified as a dog trailer. That setup tho does not work with disc brakes. Keep in mind a good kick stand will be something you will want. Something I've been doing is keeping an old pedal toe strap on my handlebar for the front brake. I tighten it up when I stop at a destination and if the front wheel doesn't turn the forks don't turn making the bike much more stable. These days there are lots of variables with bicycles and trailers these days, suspension frames, disclosure brakes, many different trailers to choose from but probably the biggest thing going is cost. If you can find a good price on a used trailer you might be able to modify it to meet your / the coop needs. I live in socal and my area for Craigs list always has something and sometimes crazy cheap. I've picked up 3 trailers from cl over the years.
Best of luck