Hunting coyotes at night is challenging but can be very rewarding. Totally disregard the comment about not using a call (total misconception). I've been hunting coyotes since I was old enough to hold a gun. Here are some sure fire techniques and rules to follow that will DEFINITELY help you out (tried and tested in many states in various areas).
#1. SCENT - make sure you are not emitting one that is easily detectable.
#2. BAIT - use a cotton tail, table scraps, almost any carcas will suffice.
#3. LOCATION - make sure you break up your sillouette if there is a moon out or other lights. Also make sure that you are not hunting down wind. And make sure that you can see for atleast 100 yards in the direction that you are intending to see the little boogers so that you can spot their eyes reflecting before they can pick up your scent.
#4. GUN SELECTION - I have found through the years that the best gun beyond doubt and question is a 22LR. If you go crazy with a large caliber it will scare off every coyote within hearing distance or atleast make them wary of coming in close enough for another shot. 22LR - not very loud, still effective out to 80 or 90 yards (used properly by a decent shooter/"hunter") and not very expensive.
#5. CALLS - USE THEM, THEY WORK CONSISTANTLY! If the coyotes get to where they won't come in for one kind of call change. The calles that I use are cotton tail distress, jackrabbit distress, fawn distress, woodpecker distress, quail distress, and sometimes even a turkey call at night (make it sound erratic like it just got pounced out of a tree by a bobcat) works pretty good.
I have more tips and information on where to find these calls and if you are interested just email me at: [email protected] and I will be glad to help you out any way I can.