https://www.chronofhorse.com/forum/forum/discussion-forums/around-the-farm/10198261-trailer-replacement-tire-question?p=10208776#post10208776 recommends Michelin XPS Rib https://www.tirerack.com/tires/tires.jsp?tireMake=Michelin&tireModel=XPS+Rib&sidewall=Blackwall&partnum=385R6XPSR&tab=Sizes
I can recommend Titan, load range D at the very least, preferably E's if you're at all close to the limit on the D's or have had any problems with them.
My trailer came with Goodyear tires, which never had problems until they started getting old. We didn't pay any attention to the brand, made sure to replace them with the same load range (D) that was on it, whatever Discount Tire wanted to sell, which was Carlisle. Blowout after blowout ensued, until this time last year, on the way back from Flagstaff, we lost *both* tires on one side of the trailer. One blew out and the flopping radial belts knocked the valve stem on the other one loose. NOT FUN!
We finally came to our senses, looked at the GVWR on the plate, at the weight rating on each tire, and then put the whole rig on a scale. (!!) It turns out my load range D tires were overloaded, especially considering the 75 mph speed limits in temps often exceeding 100 degrees out here. Also keep in mind that the trailer weight is not evenly divided over all four tires, so if you're at the limit of the tires when you add everything up, most likely at least one of the tires is carrying too much weight.
I moved up to load range E Titan tires, and had to have 15" wheels made to handle 80 PSI. We've been to California and back to pick up Patrick, to Flagstaff twice, to a bunch of lessons, and I have *finally* stopped gripping the arm rest waiting for the big explosion that means yet another tire has blown out. (And I carry two spares. :)
If I had it to do over, since we had to have wheels made anyway, I would have gone up to 16" wheels with the same lug pattern. At the time I thought the axles were too close together to allow it, but now that I've seen other trailers with tires much closer together than mine are, I know there would have been room.
Probably more than you wanted to know, but this was a very stressful time in my life and I'm glad it's over! The next trailer will have upgraded axles and 16" wheels, no matter WHAT.