I've done several hundred thousand miles towing Cobra trailers on good-quality auto / light truck tires - with no problems. I believe it is important - especially for a two-seater trailer - that the tires have the right "load index" (weight rating).

I was once persuaded to buy high-quality trailer-specific tires for my single-place trailer - expensive (about 30% more than good radial auto tires) but were claimed to be worth the premium. For whatever reason, they proved to be the worst tires I ever used - hopelessly worn after 12,000 miles. In the small town where I discovered the problem, the only tires available in my size were some alarmingly cheap off-brand auto radials that looked like they might cover the 2100 miles to home; they lasted 50k miles.