Y90 CTLR EXPERIENCED OPERROR WITH ENRTE AND CLBING ACFT AT APPROX 8000 FT.

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C130 WAS ENRTE AT 8000 FT LEVEL. C425 WAS DEP CLBING TO 9000 FT. A HDOF TO ME WAS ACCEPTED ON THE C130. C425 WAS CLBING VERY SLOWLY. I NOTICED THE C425 AT 7000 FT AT THE TIME THE CONFLICT ALERT WENT OFF. THE ACFT INVOLVED WERE OPPOSITE DIRECTION; PASSING OFF EACH OTHERS R SIDE. I ISSUED A CTL INSTRUCTION TO THE C425 TO STOP CLB IMMEDIATELY AND MAINTAIN 7000 FT. PLT DID NOT RESPOND. ON CALLING THE PLT A 3RD TIME HE RESPONDED. POINTED OUT THE TFC TO THE C130 AND HE ADVISED THE TFC IN SIGHT. WHAT CAUSED THE PROB. A COORDINATOR POS SHOULD HAVE BEEN STAFFED. SHORT STAFFING HAS BEEN AN ISSUE. THERE WERE 6 DISTRS INVOLVED IN THIS TIME FRAME THAT TOOK MY ATTN AWAY FROM MONITORING TFC. THESE INCLUDED LANDLINE QUESTIONS; A MISTAG BY ANOTHER FACILITY; A FLT OF 2 CONFLICTING WITH EACH OTHER; PLT MISSING CORRECT SQUAWK AND PLT MISSING; QUESTIONING ASSIGNED ALT. ADDITIONALLY I WAS TIRED; WORKING ON MY DAY OFF SO ANOTHER CTLR COULD GET LEAVE; VERY BUSY DAY; 3RD TIME ON THIS PARTICULAR POS WHICH WAS BUSY ALL DAY. WHAT COULD BE DONE TO PREVENT: STAFF THE COORDINATOR POS. THEY WOULD ANSWER ALL LANDLINE CALLS AND ASSIST WITH ROUTINGS AND OTHER MISCELLANEOUS TASKS. ALSO; THEY ARE AN EXTRA SET OF EYES. THIS IS A PROB BECAUSE MGMNT IS TRYING TO CUT COSTS BY NOT REPLACING PERSONNEL WHEN THEY ARE OUT SICK; THAT IS THEY WON'T CALL IN OVERTIME.