CARJ HAS TRACK DEV IN KENNEDY SID CANARSIE CLB OUT OF JFK. FLT CREW RPTS MAP SHIFT AFTER TKOF DESPITE UPDATE UPON TAKING THE RWY.

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ON THE KENNEDY9 DEP OFF RWY 31L; THE DEP WAS PROPERLY LOADED INTO THE FMS AND TO/TO WAS SELECTED IN POSITION. RWY UPDATE WAS COMPLETED PRIOR TO THE START OF THE ROLL ON RWY 31L. THE AUTOPLT WAS SELECTED ON AT 600 FT WITH SPD; NAV; AND 1/2 BANK MODES SELECTED. I STARTED THE TURN (L) DIRECT CRI VOR AT 400 FT THEN CALLED FOR THE AUTOPLT AT 600 FT WITH THE ABOVE MENTIONED MODES. THE FMS CAPTURED THE DIRECT CRI COURSE AND THEN SHOWED FMS DR. I IMMEDIATELY SELECTED UPDATE FROM NAVAID ON THE FMS TO CORRECT THE FMS DR PROBLEM. THIS OCCURRED PRIOR TO REACHING CRI VOR. AS SOON AS I UPDATED THE FMS WE SAW THAT THE MAP SHIFTED AND WE WERE 2 MILES E OF CRI VOR. I DECIDED WE WERE TOO CLOSE TO THE VOR TO TURN TOWARD IT SO I PROCEEDED ON THE OUTBOUND RADIAL 176 DEGS OF CRI PER THE CANARSIE CLB. AS SOON AS I DID THAT ATC ASKED WHY WE MISSED CRI. THE CAPT TOLD ATC THAT WE HAD A MAP SHIFT AND WE WERE TURNING TO INTERCEPT THE CRI R-176. WE WERE THEN GIVEN VECTORS AND PROCEEDED WITHOUT FURTHER PROBLEMS. ATC ALSO SAID COMPANY ACFT HAVE BEEN TELLING HIM ABOUT MAP SHIFTS ALL DAY. I WILL NO LONGER BE FLYING THE KENNEDY9 DEP IN WHITE (FMS) DATA ANYMORE. I WILL ONLY FLY IT IN GREEN (RAW VOR) DATA FROM NOW ON. I HOPE A FIX CAN BE FOUND IF SO MANY OTHER COMPANY ACFT ARE HAVING THE SAME PROBLEM.