Not sure I follow you hunter, the regs are quite clear:
"Any person may take coyotes with an unfilled big game license in the same unit and season and by the same manner of take."
So, it is legal to shoot coyotes with your big game rifle (anything over .24 caliber), as long as you have an unfilled big game license in the same unit.
However the point to my post was, why couldnt the DOWGM explain the rules to me instead of dismiss me! He has no business writing tickets or potentially arresting people if he doesnt know the rules. A GM wrote a ticket and confiscated meat from someone camped next to me cause they were in "wrong unit". The guy had to fight it in court and was exonerated, however it still ruined his hunt, plus he lost the elk meat!