You can often get the same size(or very close to it) tire for a 15" rim. If you are replacing rims/tires anyway I would try to go to a 15" rim. The reason is that 15" tires are a lot heavier duty and will last longer. Especially if you do a lot of gravel. Also you could run LT tires which will greatly increase the odds of finding a decent used set.
You REALLY don't want to run a 14" "P" rated tire on there.
A P225/70/r14 is only half the tire that a LT225/70/r15 is. Also acceptable would be an ST225/75 in a 14" or 15" tire.
P-passenger
LT-light truck
ST-special tire---trailer tire
Load ratings are important as well. LT and ST tires are usually rated, B,C,D or E. C for SUVs and 1/2tons, D for 1/2tons that are used like trucks and not cars and on 3/4ton gas models, E you will find 3/4ton diesels and 1ton trucks.
My car trailer came originally with 205/75/r15 load range C. I upgraded to 225/70/15 load rand D and have doubled the life span I get out of them. My trailer saw a LOT of gravel and I was only getting one season out of them.
Not sure how big your trailer is or how many axle it is but I would strive for a 15" rim with a load range C as the minimum.