Shooting coyotes at night with lights is a tall order but very doable. If you have a bright full moon, no clouds and snow on the ground using a scope with an illuminated dot, reticle etc - you might be in business.
No lights, full moon, no snow, coyote coming in through normal shrub brush - good luck ever seeing him.
I have a 1X8X24 Burris XTR that I gave up on and went back to my aimpoint with 2 moa red dot for coyotes, as the set-up is lighter weight and if I can see 'um, I can hit 'em out to about 250/300 yards (in daylight) - most of the time anyway.
Unless you can silhouette your target, which is very rare, night shooting is extremely difficult. Putting out road flares etc is a great way to light up the area you expect your "vermin" to pass through - only problem, they seem to shy away from everything and your only hope comes in attempting to see their eye's.
Never worked for me. Good luck in your venture.