As long as he is ONLY hunting coyotes and not even holding a big game license, there is no worry about caliber restrictions, even during big game season. Now, if he is holding a big game tag and there is a big game season going on at the time, then he would need to pay attention to the caliber restrictions then.
Had a landowner accuses my buddy and I of deer hunting, while we were only calling coyotes just two winters ago. This landowner threatened to call the game warden because we didn't have orange on and deer season was open. I told him to call the game warder real quick like because not only did we not have orange on, but neither of us held a deer tag, I was carrying an AR holding way more than 5 rds., plus my AR was in .204 cal., plus we had an electronic call. Long story short, he never called the warden because I actually think I convinced him that we were actually only hunting coyotes. He also wanted to accuse us of trespassing, but we couldn't get him to call the landowner that we were on either. I think he really just wanted to yell at someone that morning, and we were just across the fence of his property, so we got the cussin'