As far as the best to hunt them depends on sevral things, I fave time is after deer season closses and the woods calm down.
During the later part of winter ther pair'n up to mate so ther serious terratorial over intruders (other coyotes and even dogs) entering ther turf, you can learn (how to dvds) the vocal type of howls you can play it against them pretend'n to be a strange dog in ther turf look'n for love or to challenge the male for domanance and terratory.(basicaly pick'n a fight doggie style)
Spring/summer I wont hunt them, they have ther puppies and I dont see any reason for them to starve because I shot one of the pair, they need both of the parents to raise them so I leave them alone.
Fall of the year the pups are out and about and fair game,ther green in the ways of hunters and ther calls, sometimes makes for easy call'n.
Just go and try, cant tell what'll show up, plus time in the woods is wher ya hands on experience.