B190 FLC ENCOUNTER NMAC WHEN TRANSITIONING FROM MYGF TWR TO MYNN APCH CTL. PIC SUGGESTS THAT MYGF NEEDS THEIR OWN TERMINAL RADAR SYS.

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I WAS THE CAPT ON FLT MYGF-FLL; FO WAS THE PF. WE WERE CLRED FOR TKOF ON RWY 24 WITH A R TURN TO JOIN BR68V WHICH IS THE 270 DEG RADIAL FROM FZP VOR; CLB TO 6000 FT AND TO CONTACT DEP. ONCE AIRBORNE; WE STARTED THE R TURN AT 500 FT. AT ABOUT 1000 FT; I CHKED IN WITH DEP. SECONDS LATER; APPROX 1200 FT; WE RECEIVED CONSTANT TCASII ALERTS; WHICH SHOWED A TARGET OVERLAPPING WITH OUR ACFT. I INSTRUCTED FO TO RETURN TO RWY 24 EXTENDED CTRLINE. MEANWHILE; TCASII WOULD NOT CEASE WARNINGS. I CONTACTED DEP CTL TO ADVISE ABOUT THE DEV AND QUESTIONED THE TFC. THE CTLR SAID THERE WAS NO OTHER TFC RPTED UNDER HIS CTL AND THAT HE WAS NOT TALKING TO IT. I REPLIED WITH THE ALT SHOWN ON THE TCASII AS -200 FT AND 2 MI FROM FZP VOR. THE DEP CTLR ANSWERED BACK WITH CONFIRMATION THAT THE TWR CTLR HAD JUST CLRED A TFC TO JOIN THE R DOWNWIND FOR RWY 24. WE CONTINUED CLBING TO 6000 FT AND NEVER HAD VISUAL CONTACT WITH THE TFC. WX CONDITIONS WERE RPTED BY MYGF AWOS AND VISIBILITY MORE THAN 10 MI AND CEILINGS BROKEN AT FL200. THE CAUSE OF THIS INCIDENT IS THE LACK OF COORD BTWN CTLRS AND THE LACK OF PUBLISHED ARR AND DEPS PROCS THAT COULD HELP CTLRS BETTER ORGANIZE TFC ON A NON RADAR ENVIRONMENT. FREEPORT NEEDS AN APCH RADAR.