I jumped on Amazon and bought the Thule T1 Single Bike Hitch Rack. I think I might be able to mount the tray directly to the 2" square stock of the tongueIf you have space over the tongue and between the trailer and your tow vehicle, that area is probably your most viable option.
On the back of the trailer is a fairly sketchy option, anyway. Partly because hitch receivers on trailers are often built too light-duty and because the vast majority of bike racks are not built to be used there.
My trailer doesn't have a long enough tongue length for me to fit my hitch rack between the tow vehicle and the trailer. Even just carrying it folded up for later shuttling, the bike rack will make contact with the tongue tool box if I turn sharply enough. I've managed it, but it reduces my maneuverability significantly.
For now, I just use 1upUSA rooftop carriers for my bikes on the tow vehicle when I pull the trailer. A couple weeks ago, my wife took the trailer out for a weekend by herself, though. She's not strong enough to lift her bike onto the rooftop carrier, and had to shove her bike into the back of the car. And to handle bike transport duties while in camp, she had to put the hitch rack inside the camper for transport. Those options sucked, but they worked.
I need to work out something better for the next time she wants to use the camper by herself. It won't happen often, but it'll happen again eventually.
I have considered mounting a tray to the tongue. Mine's an A-frame style and there's some stuff in the way, but it might help my wife out if I did that. I have looked at putting a mount on the tongue box, but I don't think the lid of the box is strong enough.I jumped on Amazon and bought the Thule T1 Single Bike Hitch Rack. I think I might be able to mount the tray directly to the 2" square stock of the tongue