I don't lock mine either, but then, it's rare my lock-ups are in risky situations.
If I did want to, though, I'd imagine a separate cable would be an acceptable solution. The frame of the trailer is so low that you can't readily lock it with the bike's lock, and anyway, I'd be averse to uncoupling the trailer in the first place. I'd either cable it to a secure object, or lacking that, to the rear wheel.
The only other thing I can think of would be a very small diameter cable through the security strap D-ring (most trailers have one of those, right?) and around the chainstay, very much like the security strap, just secured with a small padlock.
I know people will take anything, but a kid's trailer? That's low!
