Just an FYI, Copa's newest 737-MAX aircrafts do have lie-flat business class seats. BUT, and this is a big one, COPA is notorious in doing last minute aircraft swap, meaning even if you booked a 737-MAX flights on COPA does not guarantee you will actually fly on a 737-MAX. Avoid COPA for the time being if lie-flat seat is important to you.
Without factoring the price on your actual travel dates, here are some routing/airline options in the order I would recommend. American YYZ-MIA or DFW-EZE (best frequency, relatively direct routing), Delta YYZ-ATL-EZE (relatively direct routing), Aeromexico YYZ-MEX-EZE (a bit of detour as you fly west then east), Air Canada YYZ-GRU-EZE (second segment is a fifth freedom flight, you need to deplane and GRU go through security and reboard the same aircraft), United YYZ-IAH-EZE (not daily flights, also a bit of detour). LATAM is not a bad option and probably has the most routing options, but you will have to make at least two stops (one in NA, one in SA). If driving to New York sounds better than a connection to you, you can try flying AA JFK-EZE, but that non-stop flight can be pricy.
Airlines to avoid: COPA(high chance of not getting lie-flat seat), Avianca (they are doing away business class, there is an increasing chance you book a business class now and end up flying economy), Aerolineas Argentina (their long haul business class has angled flat seat, not truly flat. This is considered dated even 10 years ago).