LTT ACFT CLBING OUT FROM CVG AND UNDER DEP CTL WHO ADVISED FLC OF VFR TFC. FLC ACQUIRED TFC AND HAD TO TAKE EVASIVE ACTION FOLLOWING TCASII REGARDING THE TFC. RPTR SAYS ALL PARTIES WERE LEGAL AND THE PROB IS CVG IS STILL CLASSIFIED AS CLASS C INSTEAD OF CLASS B.

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WE WERE CLBING OUT OF CVG ENRTE TO CHA WITH CVG DEP CTL. WE WERE GIVEN SEVERAL CLB RESTRS DUE TO INBOUND TFC TO CVG. FINALLY WE WERE CLRED TO 16000 FT. THE CAPT ACKNOWLEDGED THE CLB CLRNC AND SET 16000 FT INTO THE ALT PRESELECTOR. I VERIFIED 16000 FT AS THE CORRECT ALT AND INITIATED A CLB (I WAS HAND FLYING). DEP CTL ADVISED US OF VFR TFC AT OUR 11-12 O'CLOCK POS AT 8500 FT. THE TFC WAS ON OUR TCASII DISPLAYS AND WAS INDICATING A LEVEL ALT OF 8500 FT. WE WERE PASSING THROUGH 7700 FT AS THE CAPT ACQUIRED VISUAL CONTACT WITH THE TFC. CVG DEP WAS NOT IN RADIO CONTACT WITH THE VFR TFC. SUDDENLY; THE TCASII GAVE US A RA AS 'DSND; DSND NOW.' IN ORDER TO COMPLY; I HAD TO INITIATE A 4000 FPM DSCNT. SEVERAL REASONS CAUSED THIS INCIDENT. 1) CVG IS STILL CLASS C AIRSPACE EVEN THOUGH IT HAS OVER 600 AIRLINE DEPS (NOT INCLUDING ARRS) EACH DAY. OUR TFC WAS PERFECTLY LEGAL NOT COMMUNICATING WITH ATC. 2) THE TFC WAS A LIGHT TWIN ENG ACFT THAT; WHILE FLOWN VFR IN VFR CONDITIONS; HAD A PLT WHO WAS NOT ACTIVELY LOOKING OUTSIDE HIS ACFT. IN ACCORDANCE WITH OUR AIRLINE'S FAA APPROVED OPS SPECS; ALL LIGHTS; EXCEPT OUR TAXI LIGHT; WERE ON SINCE WE WERE BELOW 10000 FT MSL. THE SUN DID NOT PLAY A FACTOR DUE TO HIGH OVCST CLOUD CONDITIONS PRESENT THIS DAY. CVG NEEDS TO BE BROUGHT INTO CLASS B AIRSPACE OR ELSE A MORE STRINGENT TYPE OF CLASS C AIRSPACE SHOULD BE ESTABLISHED FOR ARPTS LIKE CVG.