FLC OF CPR LTT ATTEMPTING TO LAND AT UNCTLED ARPT WERE VECTORED BY ARTCC TOWARD HVY WX; DSNDED BEYOND CLRNC TO STAY VFR AND KEEP ARPT IN SIGHT UNTIL CLRED BY OVERLOADED CTLR.

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WE WERE DSNDING FROM THE W TOWARD HILTON HEAD ARPT; 49J; IN NICE VFR CONDITIONS WHEN A SMALL LINE OF SCATTERED RAIN SHOWERS APPEARED ON THE RADAR. (KEEP IN MIND WE WERE NOT CARRYING A LOT OF EXTRA GAS TO LAND ON A 4300 FT STRIP WITH 5 PAX AND BAGS IN AN SMT JET BUT ENOUGH TO MAKE SAVANNAH; OUR ALTERNATE ARPT; IF NEED BE.) IT LOOKED LIKE THE BEST DIRECTION FOR DEV WAS TO THE N AROUND A COUPLE OF SMALL CELLS AND COME IN FOR A VISUAL TO RWY 21. THE RADIO WAS BUSY BUT WE MANAGED TO GET THIS REQUEST IN TO JACKSONVILLE CENTER. IN A HURRIED MANNER THE CTLR DISAPPROVED OUR REQUEST FOR N DEV; DIRECTED A SOUTHERLY HDG TOWARD THE LARGEST CONCENTRATION OF WX AND ASSIGNED 6000 FT ALT. WE REQUESTED A VFR APCH AND HE REPLIED THAT WE COULD COUNT ON IT BUT WE PROBABLY WOULDN'T SEE THE ARPT BECAUSE OF THE RAIN. WE WERE A LITTLE CONFUSED ABOUT HIS PREDICTION OF NOT SEEING THE ARPT BECAUSE TO US IT LOOKED GOOD FOR A VISUAL ONCE WE PASSED THE SMALL SHOWER BTWN US AND THE FIELD. PASSING ABOUT 10000 FT IT BECAME APPARENT THAT THE ASSIGNED HDG AND ALT COMBINATION WOULD PUT US RIGHT IN A ROLL OF ANGRY LOOKING CLOUDS EXTENDING FROM A GROUP OF TSTMS TO THE S. WE ANXIOUSLY WAITED FOR A BREAK IN THE RADIO TFC AND ATTEMPTED SEVERAL TIMES TO CONTACT THE CTLR TO GET LOWER; A NEW HDG OR CANCEL IFR. WE HAD NO SUCCESS BECAUSE OF INCESSANT CONVERSATION WITH OTHER ACFT DIVERTING FROM SAVANNAH ARPT; WHICH WE HEARD WAS CLOSED DUE TO WX. WE CONTINUED OUR DSCNT TO 5000 FT TO AVOID THE ANGRY CLOUDS; REMAIN VFR AND REDUCE THE INCREASING TURB. FINALLY; THE CTLR GOT AROUND TO US AND ISSUED A CLRNC TO 4000 FT. BY THIS TIME WE WERE PAST THE ARPT ON THE ASSIGNED HDG AND THE AMOUNT OF RADIO TFC MADE IT A VERY CONFUSING PROBLEM TO EVENTUALLY GET OUR IFR CANCELLED FOR A VFR APCH. I DON'T KNOW WHAT WE COULD HAVE DONE TO AVOID THIS SITUATION. I DON'T FAULT THE CTLR; HE SEEMED TO BE DOING THE BEST HE COULD WITH A HAND FULL OF AIRPLANES ALL DEMANDING SVC. AND THERE PROBABLY WERE FACTORS THAT I WAS UNAWARE OF TO CAUSE OUR FLT TO COME UP ON A DEADLINE AND HAVE NOWHERE TO GO; BUT IT APPEARS TO ME THAT ATC IS OCCASIONALLY ON THE BRINK OF OVERLOAD AND ALL THAT IS NEEDED IS SOME UNFORESEEN PROBLEM TO PUT US IN JEOPARDY OR CAUSE US TO HAVE TO TAKE UNDESIRABLE ACTION.