We put up the motion sensors in a large triangle, alerted us to the coyotes. We put up a false door on the back of the house with a shooting hole, had bench and rest set up, rifle at the ready, round in the chamber, bolt up. Alarms went off at all times.
Coyotes are very protective of their food, watch for the Dominant Male that is running all the rest off, shoot him first, be patient. Then the others will come in and stay. Some coyotes are gluttons, while others like to grab a mouth full and run off.
KEY, DARK RED flood lights, come on when the sensor alerts, coyotes can not see the color red. The lighter the color red, the more apt they are to sense that "something is just not right". They can see Green, Orange, for sure. You may have to go to an arts and craft store where they sell stained glass and buy some dark red paint for the flood lights...it works.
Just shoot them in the lungs with a 22 RF, standard velocity if you have neighbor concerns. RWS Sub Sonic HP are really great for this application. We did not stick the muzzle out of the false door.
Check with your local laws to make sure this is legal.
We set up a bait trap at Sun Set, sardines in oil. We would pour several cans of sardine oil down tree trunks where the scent would really catch the wind, then just put the sardines in dog food that we bought by the 50 lb sack, scatter the dog food within the triangle, not all dumped out in a pile...make them work for it.
This will probably be an on going effort as you have to reduce the coyote population by 75% from year to year to keep the population level, and this just is not going to happen unless you are dedicated, the wife may get to where she hates being woke up by the Alert.
Best time to reduce numbers is Late July to Sept 1, yearlings are dumb as dirt, kill'em all!