ive killed them at all times of the day, they are most active at night so you will likely see them more often at dusk or dawn hours. with a 22 or shotgun you are really limited and would need to get them in close but thats easier said than done honestly you would want a hi power rifle they usually dont come in real close unless they are young curious pups and sometimes they'll come in right on top of ya. you will also need calls like a rabbit distress and a mouse squeeker the best combinatin IMO. the rabbit distress call will only get them in so close maybe 200 yards would be the closest then ya want to use the mouse squeaker it will bring them in closer also the mouse squeaker is pretty discrete as its quiet and usually wont give your position away. coyote hunting is tricky, think of it as turkey and deer hunting rolled into one. If you are really interested i suggest reading a book on it the best book ive found sofar is "Coyote hunting: from head to tail" by Phil Simonski it really covers all the basics that you need to know lots of good advise that will put ya on song dogs. good luck