APCH CTLR EXPERIENCED OPERROR AT 9000 BETWEEN CLIMBING AND DESCENDING ACFT; ALLEGING STAFFING AND COMBINED POSITIONS AS CAUSAL.

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I WAS THE APCH CTLR AT THE TIME OF THE OPERROR. I DSNDED A TEX2 TO 9000 FT WHILE AN SF340 WAS CLBING TO 10000 FT; WITH ANOTHER ACFT ENRTE AT 8000 FT. WHEN I OBSERVED THE 2 ACFT (TEX2 AND SF340) IN CLOSE PROX; I ISSUED THE TFC; AND INSTRUCTED THE TEX2 TO TURN 30 DEGS R. I THEN REALIZED THAT TURN WAS NOT GOING TO BE ENOUGH; I ISSUED FURTHER INSTRUCTIONS TO THE TEX2 TO FLY A HDG OF 180 DEGS; BY THAT TIME THE ERROR HAD OCCURRED. THE SF340 WAS TALKING TO CTR AND I WAS LATER ADVISED THE PLT OF THE SF340 RESPONDED TO A TCAS RA AND ALSO DSNDED TO WHAT I OBSERVED 8600 FT; AFTER HAVING CLBED OVER 9300 FT. THE WX WAS VMC; BUT THERE WAS NUMEROUS BUILDUPS IN THE AREA THAT ACFT WERE DEVIATING AROUND. I WAS ALSO TRYING TO WORK OUT A HDOF WITH CTR VIA AUTOMATED MEANS WITH ANOTHER ACFT AT 8000 FT; BUT THE SYS WAS RESPONDING WITH REPEATED ERRORS. THERE WERE 3 CTLRS ON DUTY AT THE TIME OF THE OCCURRENCE; ONE IN THE CTL TWR AND THE OTHER WAS ON THEIR LUNCH BREAK. I WAS WORKING THE POS COMBINED DUE TO SHORT STAFFING THAT DAY. AN EXTRA SET OF EYES COULD HAVE PREVENTED THIS FROM OCCURRING AND THE OTHER PERSON COULD HAVE BEEN WORKING ON THE HDOF ALSO. DURING THIS TIME; I BELIEVE I WAS WORKING ONLY 6 ACFT; WITH 1 DOING PRACTICE APCHS AT A SECONDARY ARPT. THE TFC IS WHAT I CONSIDER TO BE LIGHT AND HAD BEEN ON POS FOR BOUT 1 HR. IN THE END; THE CONTRIBUTING FACTORS I THINK MOST PROMINENT HERE WAS THE SHORT STAFFING AND WORKING MULTIPLE POS. DURING THIS TIME A SUPVR WALKED IN (START OF SHIFT) AND WAS BRIEFED ON THE EVENT BY ME; AS I CONTINUED TO WORK TFC.