Through July 4 and then starting again August 7 and ending December 6 there’s great availability for four passengers in business class on American’s New York JFK – Rio de Janeiro flight.
Not quite as good but there’s availability for four passengers in business class New York JFK – Sao Paulo as well, and a bit better for two passengers.
The Sao Paulo flight is operated by a Boeing 777-300ER which offers first class as well as business and there are a just handful of dates where first is available as well (this gets you access to American’s Flagship First Dining inside their Flagship Lounge). The Rio flight is operated by a Boeing 777-200 with fully flat seats and direct aisle access.
American AAdvantage charges 57,500 miles each way. Alaska charges the same. British Airways charges 75,000 — but notably these flights do not incur fuel surcharges so it’s a good opportunity to burn BA Avios, or transfer points in from Chase or American Express.