Delta has round-trip flights from New York (JFK) to Rio de Janeiro (GIG) for $523-$584, NONSTOP. Flights in October, January, and February. Very few extended weekends available. Origin/Destination reversible. Flight may operate as a LATAM code-share.
Priceline has “Express Deals” for a little cheaper, about $506 but the route Priceline route may have stops. With “Express Deals” the airline and exact flight are hidden until after purchase and those purchases are final. There is no 24-hour free cancellation for “Express Deals”. The flight is guaranteed to be on a major airline. Be sure to select the deal with 0 to 1 stops and a layover less than 3-hours.
Click for more details and booking links Nonstop Flights: New York to/from Rio de Janeiro $523-$584 r/t [Oct, Jan, Feb] – Delta / LATAM / Priceline Express