Any time American Airlines makes international business class saver award space available that’s notable, since it’s both rare and short-lived when it does occur.
From February 27 through June 24 there’s good business class award space available on American’s New York JFK – Rio de Janeiro service in both directions. Miami – Sao Paulo also has good space for 2 passengers in business class through March and April, becomes Thursdays only in May, and has decent availability again for June.