Since your question has gone unanswered and I assume the world of surviving Bubbles is rather limited, I will make a suggestion.
Take the trailer to a tire shop that handles the tire you would like to install. This assumes you are ready to install tires.
BEFORE YOU DO THAT ....
Regarding the load range, don't read too much into C or D load tire discussions if they are referring to trailers two and three times the size and weight of your trailer. That isn't a realistic comparision. You will want to match the tire's load capacity to the job to be done. So what is essential before you wip out that plastic is knowing the maximum total load of your trailer. My suggestion would be to size that total load number of your trailer to be 85% of the max tire load capacity. Then let that letter grade (C, D OR E) be what it will be.
So if the max load your trailer will ever get to is say 2000 pounds you are seeking a tire capacity of about 2400 pounds. Knowing the weight of the trailer over a scale will serve you. Add for gear, liquids and anything else you can think of if you run the trailer over the scale dry. I think you will find that a D rate tire will be far in excess of what is needed. Having too much tire can be as bad as having not enough. You want to be in that Goldilocks window of being just right for best performance.