How do you lock up your bike trailer?
I have a Burley pet/cargo trailer and when I take it to the store, I use a long (~ 3 meter) cable with a loop on the ends. I loop the one end around itself on one wheel, loop it around the hitch bar, thread it through the spokes of the  other wheel, loop it around the hitch bar again, then lock it through my bike's U-lock.

It's not super secure since the wheels have quick releases (as does the hitch bar), so it wouldn't take long enough to pop them off and untangle the cable from the hitch bar, but it's a mild deterrent against a quick "smash and grab" theft.

Plus they'd have to leave the wheels behind, which would make the trailer pretty useless, especially if the thief is going to try to sell it so he's probably not going to want to have to buy replacement wheels.

On the downside, it's just a 10mm cable, so wouldn't take much work for a thief to cut through it. 

I wouldn't want to leave it parked all day like this, but for a shopping trip with bike rack in a high-traffic location near the front of the store, it's worked out fine.