I also use the Johnney Stewart call. One thing we did that seems to have been a good idea is to put a cord of about 50 feet on the speaker. The coyote comes to the speaker. The farther away the speaker is from you, the less likely the coyote will see you or scent you since it's attention is on the speaker. You can also use this to channel the coyotes into a "kill" zone by placing the speaker in a location that makes for an easier shot. If I had it to do over again, I would get a call that played CDs and one that had remote control. I personally don't like the controls on the Johnney Stewart call. The buttons make noise and if you don't cleanly press the button, the tape drags for a second.
As I mentioned previously, we hunt in heavy cover. This way, you arn't see as easily and of course you also don't see the coyote until it is right on top of you. The action is fast and furious. Great for handgun hunting. I often use my CCW - Colt Officers Model.
I have called at night. It is very productive. The problem I have is that a lot of the time we get bobcats instead of coyotes. I personally don't want to shoot bobcats, but have done so without realizing what it was until it was too late. One trick that we have used is to drive along a dirt road (keep in mind this is in Nevada where you can drive on a dirt road for 100 miles and not see another person or house), stop and sit the caller in the road, then drive on. Wait 10 minutes and then come back. This night hunting is where I use a scoped rifle. Obviously you pretty much can't see iron sights at light. And the shots are always much further away than when we call during the day in heavy cover. A lot of times all you see is a pair of eyes.
Bobcats seem to be overwhelmed with curiosity. I have had bobcats come right into the truck at night with two of us standing there talking, both doors open, the dome light on and the engine running.
Kind of off topic, but something that I thought was cool. I was out hunting at night with a guy I worked with. We were in the mountains and saw about six deer standing on the hillside. My buddy said, watch this; he put a fawn in distress tape in his car stereo and shut off the headlights. He played the tape for a couple minutes and then turned on the headlights. The deer were all around the truck when the lights came on, sniffing at the windows.
Another thing that is very cool about predator calling is that frequently, birds of prey come into the tape and circle you at close range.
One day we were doing some calling and I got a coyote right off the bat with my Officers Model. We decided to change locations. I decided to view the whole thing from a distance to see how it would unfold. I sat up on top of a large hill about 200 yards from where my buddy set up with the caller. He turned on the caller and I spotted a coyote coming across the desert at full speed from miles away. It ran at full speed to him. It took him perhaps 10 minutes to cover the ground from where I first spotted him, and he was running then; who knows how far away he was was he heard the call initially. He ended up spooking: he ran right by my buddy at full speed and kept right on going.