So I have seen a few posts like the above, but I'm not sure if they are asking the right question.First I will assume they are really looking for tires with greater load capacity. They might also be looking for tire sizes where there are more choices in brand and Load Range. Too often the person posting the question/statement has not provided the important information on the current tires so I and anyone else trying to help, has to guess at some facts.
Lets look at a likely situation. The older trailer came with 14" wheels and possibly ST215/R7514 LR-C tires that provide 1,870# capacity @ 50 psi. These "14 inch" tires would be about 26.7" OD and 8.5" wide.
So what are the options? The easiest thing to do is to shop for Load Range D tires in the ST215/75R14 size. This would give a load capacity of 2,200# at 65 psi but with similar dimensions as the OE tire.
When making any change, I would change to bolt in metal valve stems so I can run TPMS and not have to worry about the low cost "snap-in" rubber valve stems failing.
Now if there is another reason to look for new wheels and you want to move to 15" or larger because you want a different brand tire, you MUST confirm that the new tire size can provide AT LEAST 1,870# load capacity (preferably more) AND you need to confirm that there is sufficient clearance between the new tire size and the RV frame, springs and fender skirt. Also that there is sufficient clearance between the top of the tire and the wheel well directly above the tire, and if you have tandem (two) axles don't forget the clearance between the two tires.
So one option might be an LT205/70R15 LR-E which gives 2,150# capacity at 80 psi, is 26.4 OD and 8.2" wide. The 80 psi would give a harsher ride so may not be the best choice.
An LT 215/65R16 LR-D at 1,930# and 27.0 OD and 8.7" wide might be an option.
So there are a number of options but you have to do some investigating to confirm both load capacity and physical dimensions. Some options may be better than others and there will always be some trade offs as not every size is made by every tire company so you may find a size but can't find a dealer that sells that size in your area.
A side note: Whenever replacing tires you should replace the rubber valve stems with new or bolt in metal stems for improved reliability even if you don't run TPMS. Once you make the switch to bolt in metal valves, I doubt if you will need to change the stems for the life of the next two sets of tires.