CAPT OF A B737-500 FAILED TO FOLLOW THE SID DEP TRACK TRANSITION DUE TO USING THE WRONG FMC MODE SELECTION.

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DEPARTED JFK RWY 31L. ROUTING WAS KENNEDY 7. BREEZY POINT CLB; DIRECT RBV; J230 BYRDD. I SELECTED (DURING PREFLT) KENNEDY 7 DEP FROM FMC DATABASE (NO TRANSITION AVAILABLE IN DATABASE) THEN PROGRAMMED REST OF RTE INTO FMC (RBV; J230 BYRDD...). WHEN FO RETURNED FROM PREFLT WALKAROUND; I REQUESTED THAT HE VERIFY THE PDC AND FMC; WHICH HE DID. AT THE GATE (PRIOR TO PUSH) AND DURING TAXI OUT; I BRIEFED THE KENNEDY 7. BREEZY POINT CLB. PRIOR TO TKOF; I DECIDED TO USE LNAV AT 400 FT INSTEAD OF USING HDG SELECT AND VOR LOC MODE. LNAV WORKED FINE; DIRECTING ACFT TO CRI VOR. HOWEVER; AFTER CRI VOR WE WERE REQUIRED TO FLY OUTBOUND ON THE CRI 223 DEG RADIAL. FMC WAS PROGRAMMED TO FLY DIRECT TO RBV AFTER CRI. SHORTLY AFTER PASSING CRI VOR; DEP CALLED AND TOLD US TO TURN TO A HDG OF 190 DEGS AND INTERCEPT THE CRI 223 DEG RADIAL. FMC DID EXACTLY WHAT IT WAS PROGRAMMED TO DO. I FAILED TO INSERT A FIX THAT WOULD ALLOW THE FMC TO FLY OUTBOUND ON THE CRI 223 DEG RADIAL (IE; 223 DEGS/10 DME WAYPOINT) AND MY FO DID NOT CATCH THE MISTAKE. I ALWAYS DOUBLECHK THE ROUTING; ESPECIALLY ALL DEP AND ARR FIXES. SOMEHOW I OVERLOOKED A CRI 223 DEG FIX. PART OF THE OVERSIGHT WAS CAUSED BY RUSHING (WE ARRIVED A LITTLE LATE FOR DEP). THE OTHER PART WAS THE FACT THAT THE FMC DID NOT OFFER A TRANSITION AFTER THE CRI VOR. THIS SHOULD HAVE RAISED A RED FLAG. ADDITIONALLY. I ORIGINALLY PLANNED TO USE HDG MODE AND VOR/LOC MODE FOR THE DEP. ON TAXI OUT; I CHANGED TO VISUAL LNAV (NEVER CHANGE CODES IN THE MIDDLE OF THE STREAM).