Though it would still be fascinating to know how U.S. cowboys who wanted it on the down-low came to know that Mexico was the place.
Well, I think traditionally Mexico has been the place for a lot of things that are harder to obtain in the U.S.: quickie divorces, marijuana, questionable medical procedures ...
You can walk across a bridge from El Paso to Juarez. Juarez is pretty poor and, according to stereotype, less strictly policed (or at least the law-enforcement is less by-the-book). So from an economic standpoint, industries that cater to American no-nos are probably a natural consequence.
Still, how did Ennis know about it so specifically? I can't imagine his coworkers, when exchanging travel tips, recommending it as a destination for sex tourism. But maybe they would taunt each other with the "You been to Mexico?" line.