Bus will usually be your cheapest option. Greyhound is probably somewhere around $35 each way, but you gotta get your cousin from JFK to Port Authority bus station in Manhattan. Taxis into Manhattan will run you about $50. Alternatively, you can take the AirTrain out of JFK to connecting MTA subways that go into Manhattan. IIRC the AirTrain is $5 and the subway is $2.