What works on a smaller/lighter trailer doesn't work so good on our larger trailers like your 36' Cameo so take recommendations of any ST tire with a grain of salt.
You will get a much better response by giving us the OEM size and your trailer axle ratings.
Generally....
... on 6k axles and smaller the 16" LT E at 3042 lbs capacity is a excellent upgrade with Bridgestone R250 and Michelin XPS Rib on top. Both are a commercial grade all steel ply carcass tire.
If your trailer has 7k axles then the Goodyear G614 and the Sailun S637 in a LT235/85-16 G load range at 3750 lb capacity. Both are a all steel ply carcass construction.
And many folks 7k/8k axles under their trailers move up to the 17.5" wheels and commercial grade LT tires.