Pretty hard not to get a radial these days. Usually sway is caused by improper loading, not enough hitch weight, too much tail weight.

Most trailers tires(ST) rating are built with stiffer side walls to counteract side wall flex. Myself personally I prefer to run LT truck tires with a D or E loading rating depending on the trailer. I find I get MUCH longer life out of a trailer tire that way.

NEVER, ever put a P rated passenger tire on a trailer. I've seen those pop the beads on a hard turn from the sidewall flex.

 

To build on the tire info a bit: Trailer tires are different than vehicle tires, the sidewalls are stiffer, and they come in different load ranges in the same size. The give-away for a trailer tire is the letter "T" in the tire size: ST205/75D15 for bias ply trailer tires and ST205/75R15 for radial ply trailer tires. Radial ply trailer tires have the same advantages as vehicle radials, the disadvantage being higher initial cost. Make sure your trailer tires are 'T' type, have adequate tread, are not dry or cracking, and are inflated correctly for the load. I wouldn't run a vehicle tire on a trailer, regardless of load range, YMMV.

http://accessories.etrailer.com/sear...tiresandwheels

http://www.discounttire.com/dtcs/inf...rTireFacts.dos

http://www.taskmasterproducts.com/ac...ailertires.pdf

 

Trailers that sway are caused by to low of a tongue weight on the tow vehicle, not radial tires. Most trailer tire are radials now and stamped for trailer use only!