We were given some airless tires a few years ago by two different manufacturers to test on some bicycle trailers. Our experience was the tires performed find when the trailers were empty, but the rolling resistance was noticeably higher than a pneumatic tire when the trailer was loaded--so much more, in fact, that we discarded them immediately after the test.

I think the best solution is to use pneumatic tires with a Kevlar liner built into the tire casting.