If you don't plan on keeping the hides, anything that will kill them will work. I use a .223 myself with any bullet with rapid expansion. I like a bullet that will expand or fragment on impact so that it does more damage to the vitals and provides for quick drops. As for timing, I do most of my calling in the early morning hours or later in the evening. I don't do much at night because I like to get to bed at a reasonable hour. I carry a good set of binoculars stick a mouth call in my front shirt pocket. I don't always wear camo, but I do try to wear stuff that's not seen too easily. Then I go out, pick a spot where I can see a good ways downwind and start calling. The coyotes nearly always come in from downwind because they can smell a lot better than they can see. The sound also travels downwind a lot further. I blow on the call four or five times and then look around continuously with the binoculars for about five to ten minutes. Then I call again and keep scanning. I'll stick to the same spot for about thirty minutes. If nothing shows, then I move on. If I shoot something, I keep calling until thirty minutes after my last shot. That gives any other coyotes in the area time to gather themselves and come in for an inspection if the shot startled them.