PLT OF A BELLANCA ENTERED THE TFC PATTERN CONTRARY TO ATCT LCL CTLR'S INSTRUCTIONS CAUSING AN NMAC WITH A BEECH DUCHESS ON A DOWNWIND LEG IN THE OPPOSITE DIRECTION. THE DUCHESS MADE A STEEP CLBING TURN TO AVOID THE BELLANCA.

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THE PLT OF THE BELLANCA RPTED OVERHEAD THE ARPT AND WAS INSTRUCTED TO MAKE R TFC FOR RWY 21R AND TO RPT A 2 MI 45 DEG TO THE DOWNWIND. HE ADVISED THAT HE NEEDED TO LOSE ALT AND WAS INSTRUCTED TO PROCEED W OF THE ARPT AND MANEUVER FOR THE R 45 DEG FOR RWY 21R. THE BELLANCA PLT READ BACK 'R 45 DEG FOR RWY 21R.' THE BELLANCA PLT RPTED R BASE AND THEN CORRECTED HIMSELF AND SAID HE WAS NOW ENTERING DOWNWIND OPPOSITE THE TWR. ATC PERSONNEL HAD BEEN LOOKING FOR THE BELLANCA WITHOUT LUCK; AND THERE WERE MANY ACFT IN THE AREA AND PATTERN. THE BELLANCA SHOULD HAVE BEEN VISIBLE AT THIS POINT. I LOOKED TOWARD THE OPPOSITE DOWNWIND (L DOWNWIND) BACK AND OBSERVED THE DUCHESS MAKING A STEEP; CLBING; R TURN TO AVOID COLLISION WITH THE BELLANCA THAT WAS OPPOSITE DIRECTION TO THE L DOWNWIND FOR RWY 21L. THE BELLANCA WAS ON A R DOWNWIND FOR RWY 3R INSTEAD OF R DOWNWIND FOR RWY 21R. PRESCOTT TWR WORKS 350000 OPS PER YR WITHOUT ANY RADAR. WE WORK UNFAMILIARS INBOUND 10% OF THE TIME AND MANY DON'T ENTER WHERE THEY ARE SUPPOSED TO BE; BUT MOST ARE LUCKY AND DO NOT END UP CLOSE TO OTHER ACFT.