CARJ FLT CREW MISPROGRAMS CANARSIE CLB ON THE KENNEDY DEP FROM JFK.

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THE CLRNC WAS KENNEDY 9 DEP; CANARSIE CLB (OFF OF RWY 31L); COATE INTXN; AS FILED; CLB AND MAINTAIN 5000 FT; EXPECT FL220 IN 10 MINS; SQUAWK XXXX. I WAS THE FO AND THE CAPT WAS THE PF. HE BRIEFED HIS TKOF AND DEP; HOWEVER; THE FMS HAD BEEN PROGRAMMED TO GO TO COATE AFTER CRI VOR. THIS WAS INCORRECT AS THE CANARSIE CLB REQUIRED US TO TRACK OUTBOUND ON THE 176 DEG RADIAL AFTER XING CRI VOR. ON THE GND; WE VERIFIED THE FLT RTE BY THE CAPT SCROLLING THROUGH THE LEGS PAGE OF THE FMS AND I VERIFIED EACH POINT FROM THE RELEASE; HOWEVER; WE STILL MISSED AN IMPORTANT PART OF THE CANARSIE CLBOUT. AT APPROX 5000 FT WE WERE APCHING CRI VOR AND THE AUTOPLT BEGAN TO TURN THE ACFT DIRECTLY FOR COATE. THE CAPT TURNED OFF THE AUTOPLT AS HE REALIZED THIS WAS AN INCORRECT TURN. AT THAT MOMENT ATC QUERIED US AND ASKED US TO TURN IMMEDIATELY TO A SOUTHERN HDG AND THEN ADDITIONALLY TOWARD THE E AS HE CLRED US FOR HIGHER ALTS. BY THE TIME WE WERE HANDED OFF TO CTR; ATC ASKED ME TO COPY A PHONE NUMBER FOR TFC MGMNT. UPON OUR ARR IN PIT; THE CAPT TELEPHONED TFC MGMNT. I WAS UNAWARE OF THE EXACT CONVERSATION; HOWEVER; THE CAPT TOLD ME THAT ANOTHER FLT HAD COINCIDENTALLY DONE THE EXACT SAME THING MINS BEFORE US. HE ALSO SAID THAT NO FURTHER ACTION FROM US TO ATC OR THE FAA WOULD BE REQUIRED. WHEN THE CAPT DEACTIVATED THE AUTOPLT; I AM UNCERTAIN IF HE KNEW WHERE HE WAS TURNING OR IF HE KNEW THE CORRECT HEADING. NEITHER OF US HAD THE 176 DEG RADIAL OFF OF CRI VOR UP AND WE WERE BOTH IN WHITE DATA. I HAD TOLD THE CAPT PREVIOUSLY ABOUT THE CANARSIE CLB IN OUR CLRNC; HOWEVER; HIS TKOF AND DEP BRIEFING DID NOT INCLUDE THE CANARSIE CLB. FURTHERMORE; I DIDN'T ASK WHAT HIS INTENTIONS WERE DURING THAT CLBOUT AND ASSUMED ALL ITEMS OF THE DEP WERE DISCUSSED.