If you don't want to use Uber and Lyft which are most comfy ones and not too expensive, then public transportation is the way to go but you would need to do a couple of transfers I am afraid.

Take the AirTrain to Jamaica Station, go to the ground floor where the connection to the Subway is available. Hop on the E train, To Manhattan and hop off at Port Authority Bus Station. There you have the bus line 163 that goes to Paramus. Bus ride is approximately 15-20 minutes on the express bus. Total cost will be around $15

Las time I ride an Uber to Tenafly from JFK it cost me $70, George Washington bridge toll included. It was at 20:00 approximately.