I don't think this has ever been done before for a lightweight bike trailer, which would mean no, there aren't any proven approaches to using surge brakes on a bicycle trailer, but I've got some ideas...
It would be very impractical to use any current trailer surge brake options on a bicycle trailer, they'd be too clunky, heavy and wouldn't be compatible with bike hitches. An alternate solution for braking would probably be more practical (extra lever on the handlebars), and less likely to fail, but I'll address your question as you've asked it; which means we're talking about engineering something completely new. Things you have to consider:
- Trailer - I think it's important to start with the trailer you plan on using, then think about how to modify it. I recommend something with a hitch like the Woody Wagon Canoe Bicycle Trailer:
Brakes - Obviously you're going to have to go with hydraulic disc brakes, because cable brakes would have way too much stretch in them. The first thing you have to figure out is how to mount your brakes on the tralier. The ideal solution would be to buy some Chariot disk hubs like they use on their CX-1 trailer. You'll also need a hose splitter to operate both callipers with one lever.
Actuation - This is going to be your biggest hurdle, and really what your question is all about. You could easily mount a stock brake lever to your hitch (likely with a customized lever), you just need to come up with a method of operating it with a custom made surge brake actuator.
Here's my concept for what I think would work best:
This is obviously a very simple illustration - use parallel hinges to 'hang' the trailer hitch from a receiver mounted to your seat post. Put the brake lever on the receiver, and let pendulum action from the momentum of the trailer actuate the brake lever.
You'll of course have to take wheel and cable clearance into consideration, and you'll have to calculate what hinge length will give you effective actuation, and actually connect the pendulum part to the lever in some way–and other fine details, etc... But theoretically, I think this would be the easiest, simplest, and most effective method of putting surge brakes on a bike trailer.
Some good comments gave me some ideas for already improving on my concept. I moved the brake to the trailer side of the parallel hinges–which offers more tire clearance and keeps it out of the mud coming off the tire–and I simplified it by actually making one of the hinges double as the brake lever.
Another consideration is to be sure the wheels are secured to the canoe well enough that they don't get pulled out from underneath when the brake engages and rip your hydraulic hose out of the callipers/lever. Either a long bar to connect the hitch to wheels, or a long strap to prevent the wheels from sliding back could be necessary if the trailer wheels can't be adequately secured to the bottom of the canoe.