"Likewise, simply dropping by with a Great Pyrenees dog is totally worthless."
Mobuck is right here. I didn't go into detail,, as I figured this wasn't really an option. I was adding to the info about what many serious ranchers do to protect livestock. But the dogs have to trained,, as Mobuck does.
Ok, by now,, you have seen that trapping isn't really a good option UNLESS you get a pro. And if you try that route, check credentials,, and past experiences. Someone who is a serious fur trapper,, AND targets coyotes is a good start,, and not (usually) expensive. They want the fur. Sadly, in Ga. the fur isn't worth much, as compared to other areas. A pro like myself,, well it can cost a lot for one to spend the TIME necessary to do it right. I OFTEN advise my customers to spend the money instead, on a good fencing system. I say again,, a GOOD fencing system. There is a trick or two to building a fence that can keep a coyote out. And it can be done w/o using electric fencing. But adding electric to it is a good idea & helps.
" In the evenings she puts them on her back porch which is railed & about 4 feet above the ground with the access from the stairs blocked. She said they were trying to get onto the porch."
Ok, the 4 ft raised part helps. Adding an electric fencing to this, on the outside all around the porch will be an excellent idea. Then, where the stairs are,, that's where the yotes will try harder to get over, or around. It concentrates them to that point. That can be both a problem AND a blessing,, depending upon what you are trying to do. If I were to do this job,, I'd first recommend the electric for the porch area,, and then, I'd set multiple traps (using ALL the necessary methods of scent control & hiding them I know,) all around the base of the stairs. And,, I'd also add a moveable (for me,) barrier made of a metal gate, barbed wire, and a separate electric fencing set-up to make the yotes that get past the CAREFULLY set traps below. All this takes work, time & knowledge.
PS; Scent control. If at all possible,, using the urine from her dogs is an excellent cover scent around the traps. Getting it where you need it is the hard part. If she has a place that a dog or two likes to pee,, and it not soak into the ground etc,,a syringe needle can suction it up, and it be moved to the area necessary. Or,, the indoor pee pads,, if used,, can be placed in a plastic container, adding a little water to them, and using gloves,, squeeze out the fluids,, using that. Again, a syringe is helpful here to prevent human scent on things. Application of this pee is also important,, but it can help cover human scent with a familiar scent they already know.
But traps do require a proper knowledge in how to build trap sets,, making them effective. If I were to set up on this,, from your description, I'd likely add about a dozen,, properly placed,, with drag poles to allow the caught ones the ability to move away from the other traps to hopefully get a multi-catch. As noted above,, miss a coyotes with improper trapping & you just educated it.
Re-read that again; Miss a coyote with an improper trap, and you just educated it!
So, in this scenario, electric fencing around the porch, and a proper barrier with electric would likely be the best option. Construct it so it's a permanent thing. BECAUSE,, if you deter the current ones right now,, they can & will return later to see if they can overcome things. And if not,, their relatives will sometimes move in & make an attempt at the little dogs.
I call this; "Co-existing with a problem to where the problem figures out I'm not worth the trouble, and goes elsewhere. But always be vigilant as the problem can & will try & return."