I know a Brit who has done well with rentals in Lima. He's married to a Peruvian and they have about 16 apartments well situated in Miraflores. By now he doesn't have to advertise since much of his business is repeat customers. He takes down payments through Paypal, which is convenient for Americans.
Not a bad business for cities that attract both tourists and business travelers, like Lima, Bogota or Medellin.