Calling is the most productive method of hunting coyotes. Electronic calls work, but so do much cheaper and easy to carry mouth blown calls. There is a lot of information out there about calling coyotes if you look for it, or search this forum. Google is your friend, and there are many different techniques that will work. Research and experimenting are essential.
I have posted this on this forum before, and I apologize to those who saw it already, but I'll stick it here once more as a "starting point" for advice.
The first rule of coyote hunting is to hunt where there are coyotes.
We call coyotes that have been called before and not killed "educated" coyotes. If yours are educated, and hunting pressure will educate many for sure, they will be very hard to call. You may have to try something "different" to get their curiosity aroused. That is a very wide topic, so I will stick to generalities we use as SOP.
If they know you are there, they will not come. No sky lining; no walking across open areas if possible; stick to edges; use depressions; do not be easily visible from far away at any time.
No noise. You are going to call an animal with a sound, so don't make any noises that sound like coyote hunters. No talking; no slamming truck doors; no noise you can avoid; approaching the area while keeping a ridge between you and the area masks sound well.
Control your scent plume so it does not enter the area you intend to call to. We do not use any scent masking soaps, sprays, clothing, or whatever, because we believe they are useless and the only way to avoid a coyote's nose is to not let him smell you. One exception is we will often deliberately allow our scent into an open area down wind. Often coyotes will circle down wind to get a smell of what's making the noise. If the open area is large enough, they must expose themselves to do so. Often, in that moment they get your scent, they will stop to think it over for a few seconds. THAT is a good time to shoot, because they will likely leave after they decide what you are.
Break up your outline somehow. Brush in front (as long as you have a shooting lane) or behind you will do that. Do not move around any more than you must. We like to hunt in pairs. One guy gets fairly hidden, sometimes giving up long range vision, and does the calling. The other sets up to cover the approaches from an angle that allows him to see well, but the animal will be looking elsewhere for the source of the sounds. Decoys can work for this distraction too, if you are alone.
We use mouth calls exclusively. We walk lots and we hate carrying crap. That's the only reason to avoid the electronics that we can think of; that and the cost, and cold batteries. We have howlers, but use them mostly for "location" calls and then move in and use "dying prey" type calls. We believe only dominant animals will really approach a stranger in their territory, so howlers are less productive than prey type calls. We want the insecure ones too.
Call "softly" the first time in case they are close; you don't want to scare them. We call for 30 seconds to a minute and then sit for 5 and watch. The next set of calls can be louder. Watch very, very carefully. Binoculars are a real help, even in the bush. You cannot pay too much attention. Around here, if you see a magpie coming to the call, pay close attention to that direction. Coyotes and magpies hang out a lot together. Pay attention to the really unexpected directions too. Make head movements slow and steady rather than quick glances. Move nothing more than you have to.
The length of time we call a particular set up depends on how long we think a coyote would take to come from the farthest ranges we think the call is reaching. Wind knocks down calls really quickly, so your range is short. Calling from a ridge on a calm evening will reach a long way. Experience is likely the only teacher here. We have had coyotes over half an hour into the set, but most of the time 15 minutes will tell you what you need to know. Be very careful once you decide the set is done. Stand up slowly and have a long look around. The new angle will reveal all those coyotes you called but have not yet seen (and there will be a depressingly large number of them). You may get a shot if you don't create too much of a spectacle so that the dog has to figure out what the H*** just moved. But chances will not last long.
If you are going to just move and try again, don't talk, don't make noise, don't expose yourselves any more than you must. They may be watching. We move far enough to enter a "new" area that we think holds animals that have not yet heard us. In a big wind that may not be far; on a calm day that may be half a mile or more. We avoid calling the same area more than a couple of times a winter. Educated coyotes and all that.
Shooting sticks or tripods are essential. We use .22-250s or .243 and one 6mm Rem as dedicated coyote rifles. Coyotes are, pound for pound, a very tough animal. They are also small targets. You need to be able to shoot well, and shoot quickly at times with some honest power too. Multiples get really interesting. We agree before hand about left side/right side etc. and who will shoot first.
