If your payments to a property owner are "in the course of your business or trade," and they are more than $600 in a year, then yes. However, if the party to whom you make payments is a corporation, you are exempt from the requirement to issue a 1099. Perhaps the party to whom you pay the rent is obligated to file a U.S. tax return? Whether or not, it couldn't hurt to issue a 1099 and report via a 1096.
