A C208B CHARTER PLT EXPERIENCED SELF-DOUBT AFTER LNDG AT MYAM AT NIGHT WITHOUT BENEFIT OF ARPT LIGHTING.

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I DEPARTED FLL IN A C208B WITH 9 PAX; ENRTE MYAM IN THE BAHAMAS. BEFORE DEP; DISPATCH ASSURED ME THAT ARRANGEMENTS WERE MADE WITH BAHAMAS AUTHS TO HAVE SPECIAL PERMISSION FOR A NIGHT LNDG AS WELL AS RWY LIGHTING; CUSTOMS; AND IMMIGRATION TO HANDLE THE ARR. TIME OFF AT FLL WAS AT ABOUT SUNSET FOR THE AREA. UPON ARR NEAR MARSH HARBOR; I HAD DIFFICULTY IN LOCATING THE ARPT; SINCE IT WAS VERY DARK; A BIT MORE THAN 1 HR AFTER SUNSET AND THE PROMISED RWY ILLUMINATION WAS NOT PROVIDED. I MADE 3 ATTEMPTS TO LAND. THE FIRST WAS ABORTED EARLY AT ABOUT 800 FT AGL BECAUSE I LOST SIGHT OF THE RWY. ON THE SECOND ATTEMPT; I REJECTED THE LNDG BY APPLYING TKOF PWR WITHIN APPROX 50 FT OF THE SURFACE BECAUSE OF HIGHER THAN EXPECTED APPARENT SINK RATE AND MISALIGNMENT WITH THE RWY. BOTH MAIN WHEELS MADE CONTACT WITH THE RWY MOMENTARILY BEFORE THE ACFT BEGAN TO CLB. ON THE THIRD ATTEMPT TO LAND; I SET UP FOR AN APCH TO THE OPPOSITE (RWY 27). THE RAMP AREA ADJACENT TO THIS RWY MADE IT EASIER TO IDENT THE TOUCHDOWN ZONE. THIS TIME THE LNDG WAS MADE. I TAXIED THE ACFT TO THE RAMP AND COMPLETED THE DEPLANING OF PAX AND UNLOADING OF BAGGAGE. AFTER LNDG I BEGAN TO REFLECT ON THE FLT AND THE REPEATED APCHS TO THE UNLIGHTED RWY. ALTHOUGH THERE WAS NO INJURY OR DAMAGE TO ANYONE OR ANYTHING; THE REALITY OF THE DANGEROUS SIT I HAD PUT US IN BECAME CLR. IT ALSO BECAME CLR TO ME THAT A RETURN TO FLL WAS WHAT SHOULD HAVE BEEN EXECUTED AS SOON AS IT WAS DISCOVERED THAT NO RWY LIGHTING WAS IN USE. I FELT; AS I DO NOW; THAT I HAD FOCUSED AND FIXATED ON THE MISSION OF DELIVERING MY PAX TO THEIR DEST. I SHOULD HAVE FOCUSED INSTEAD ON OUR SAFETY.