PA28 PLT DESCRIBED NMAC DEPARTING RWY 13 AT CYS CONFLICTING WITH KING AIR ENTERING DOWNWIND FOR RWY 27 AT 7200 FT; NO TFC ISSUED BY ATC.

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I PLANNED A DEP FROM CYS IN A PA28R ARROW. THE FIRST WAYPOINT WAS THE MBW VOR. THERE WAS A NOTAM FOR MIL AIRDROP ACTIVITY 9000 FT AND BELOW AND 3 MI EITHER SIDE OF A LINE FROM CYS349027 TO CYS256012 TO CYS216014. SINCE THIS BLOCKED A DIRECT DEP TO THE NW TO MBW; I PLANNED TO DEPART TO THE N; REMAIN E OF THE CYS 360 DEG RADIAL; AND CLB TO A SAFE ALT ABOVE 9000 FT BEFORE TURNING NW. I REQUESTED A N DEP WHEN I CONTACTED CHEYENNE GND. ATIS INFO RPTED WIND 180 DEGS AT 6 KTS AND GND SENT ME TO RWY 13. WHEN CHEYENNE TWR CLRED ME FOR TKOF; THEY STATED L TURNOUT APPROVED. AFTER TKOF; I CLBED ON RWY HDG UNTIL I WAS AT ABOUT 600 FT AGL THEN BEGAN A TURN TO THE N. I SET UP FOR A VY CLB AT 90 KIAS. AS I APCHED THE EXTENDED CTRLINE FOR RWY 27 AND ABOUT 0.5 NM E OF THE RWY 27 THRESHOLD; A KING AIR RPTED ENTERING R DOWNWIND FOR RWY 27. THE TWR DID NOT RESPOND TO THE KING AIR INSTEAD TALKED TO A BEECH 1900 ON THE GND. I LOWERED THE NOSE FOR BETTER VISIBILITY AND BEGAN SCANNING FOR THE KING AIR. I GLANCED AT THE ALTIMETER AND SAW 7100. TFC PATTERN IS 7200 FT MSL. I LEVELED OFF AND INITIATED A GRADUAL DSCNT. ONCE THE FREQ CLRED; THE KING AIR AGAIN CALLED R DOWNWIND FOR RWY 27. DURING THAT XMISSION; I SPOTTED THE KING AIR AT MY 10:30 O'CLOCK POS; SLIGHTLY ABOVE ME; AT ABOUT 1/4 MI AND CLOSING. I IMMEDIATELY PUSHED THE NOSE DOWN. AT THAT TIME TWR ACKNOWLEDGED THE KING AIR AND ADDED TFC IS AN ARROW. AT ABOUT THE SAME INSTANT TWR COMPLETED THE XMISSION; I PASSED DIRECTLY BENEATH THE KING AIR WITH LESS THAN 200 FT VERT SEPARATION. THEN TWR CALLED; SORRY ABOUT THAT ARROW XYZ; TFC IS A KING AIR ON DOWNWIND. THE TRACK NODE AT THAT TIME SHOWS A GND SPD OF 122 KTS; WHICH I ASSUME WAS DUE TO THE RAPID DSCNT TO AVOID THE KING AIR. THE KING AIR PLT LIKELY DID NOT SEE ME. I WOULD HAVE BEEN AT HIS 1 OR 2 O'CLOCK POS AND SLIGHTLY BELOW. THIS MAY HAVE PUT ME BELOW HIS GLARE SHIELD. I DID NOT NOTICE THAT HE TOOK ANY EVASIVE ACTION AND HE LANDED ABOUT 1 MIN LATER ON RWY 27. HE DID NOT COMMENT ON FREQ ABOUT THE NEAR MISS. ONCE I HEARD THE KING AIR ANNOUNCE ON R DOWNWIND; I DID RECOGNIZE THE SITUATION THAT WAS DEVELOPING AND I SHOULD HAVE REACTED SOONER BY IMMEDIATELY CHKING ALT AND STAYING WELL BELOW PATTERN ALT. CHANGING COURSE WOULD HAVE ALSO BEEN AN OPTION; BUT EVEN NOW I DON'T KNOW WHICH DIRECTION WOULD HAVE BEEN THE BETTER CHOICE. PERHAPS THE SINGLE MOST IMPORTANT REASON THAT I FAILED TO ACT SOONER WAS MY ASSUMPTION THAT THE TWR CTLR WOULD PROVIDE TA'S. I DO RECALL THINKING TO MYSELF; WHY ISN'T TWR RESOLVING THIS? I THINK THIS ASSUMPTION IS A FUNCTION OF MY INEXPERIENCE; IN GENERAL; BUT ALSO FROM COMPLACENCY BASED ON THE EXPERIENCE THAT I DO HAVE. MY HOME FIELD IS IN CLASS D AIRSPACE AND I HAVE GROWN ACCUSTOMED TO MY LCL CTLRS BEING VERY CAUTIOUS AND PROVIDING PLTS WITH AMPLE TFC CALLOUTS. I NOW HAVE A BETTER UNDERSTANDING THAT TFC AVOIDANCE UNDER VFR IS ULTIMATELY THE PLT'S RESPONSIBILITY AND NOT THE CTLR'S. HAVING SAID THAT; I DO BELIEVE ANOTHER LINK WAS THAT THE TWR CTLR DID NOT RECOGNIZE THE SITUATION DEVELOPING. IF THE KING AIR HAD CALLED UP BEFORE I TOOK OFF AND WAS EXPECTED ON A R DOWNWIND FOR RWY 27; TWR SHOULD PROBABLY NOT HAVE CLRED ME FOR A L TURN AND DEP TO THE N. SIMILARLY; THE CONCERN OVER THE BEECH 1900 ON THE GND SUGGESTS THAT TWR WAS UNAWARE OF THE SITUATION DEVELOPING IN THE AIR.