First, coydogs and coyotes are two different animals. 200yds is way past the 22mag range and unless I am absolutely sure of the back stop, I do not use a centerfire rifle at night. I set 100yds as my limit for night shots, because with a good light I can see what is attached to those two glowing eyes. At that distance a 22mag with the 1.5x5 lit reticule would work fine. Coyotes have the advantage during the day, multiply that by 100 at night. Get a Cass Creek electronic predator call. They work great.
At night, coyotes usually come to the call in pairs, the coyote that you see and the one that is already circling around you to see what is making the sound. When starting out 9 times out of 10 you will be found out before you ever see them. When you hit them with the red light, you have just a couple of seconds to get off the shot because now they know where you are. Your first outing should be under a full moon so you can see better, but remember, he can also see better. Wear full camo like you would turkey hunting.
Good luck, you will need it!