DEP CTLR AT CVG ISSUED A LATE CLB INSTRUCTION TO A SLOW CLBING CARJ ACFT RESULTING IN A LOSS OF SEPARATION WITH AN MD80.

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THE CARJ (RJ) WAS TURNING FROM 290 DEG HDG CLOCKWISE TO 320 DEG HDG; TO LEAVE 6000 FT AND CLB TO 13000 FT. THE MD80 WAS ON 240 DEG HDG AT 230 KTS LEAVING 5300 FT FOR 6000 FT. THE RJ WAS AT 250 KTS (SURFACE WIND 070 DEGS AT 11 KTS). AT A POINT WITH 4 NM HORIZ/700 FT VERT; THE RJ WAS TURNED FROM 290 DEG HDG AND CLBED. THE 240 DEG HDG VERSUS 320 DEG HDG WOULD PROVIDE APPROX 1 1/2 - 2 NM AT THE CLOSEST BTWN ACFT. THE RJ DELAYED THE CLB; LATER CLAIMING TO BE 'JUST USING THE AUTOPLT?' WITH THE CARJ PASSING THE 12 O'CLOCK POS AND 3 MI; THERE WAS 300 FT DIFFERENCE IN ALT (MODE C'S). THE CARJ WAS THEN ON THE 320 DEG HDG AND THE MD80 HAD JUST LEVELED OFF; AND ADVISED ME OF THE TCASII EVENT WITH THE CARJ 'JUST OFF THE NOSE.' TFC HAD BEEN CALLED BTWN ACFT; AND THE MD80 HAD THE CARJ IN SIGHT. CHAIN OF EVENTS: RWY CHANGE IN PROGRESS; COORD/DISTR WITH THE SIT OF A NEARBY ARR ACFT CAUSED ME TO NOT HAVE ISSUED HIGHER TO THE CARJ SOONER. I THOUGHT I HAD DONE THAT (CLB THE CARJ) PRIOR TO THE 4 MI DEVELOPMENT. I MUST HAVE OBSERVED MODE C 5700 FT ON THE CARJ; CONFIRMING THAT 6000 FT COULD BE ISSUED TO THE MD80. ALSO; THE 2 ACFT INVOLVED NEEDED 'IN-TRAIL' SEPARATION OUT THE SAME DEP GATE AND THE TWR HAD BASICALLY DEPARTED THEM OFF DIFFERENT RWYS; RESULTING IN A 'TIE' -- IE; HIGHER COMPLEXITY.