Just wait. See what thw coyotes do at the carcass. When they start feeding Then put out traps. Most ol timers will telk you = its best to wait till the coyotes start feeding on carcass THEN put traps out accordingly
Heed the advice given above. And if you do trap around it intercept the coyotes as far away as you can from the carcass to keep the spot producing. I'll set 200 or 300 yds away here. If your going to cut meat of the cow don't do it were u dump it. Personally I wouldn't waste my time or leave my scent on the carcass cutting bait off it. Not that good of bait. A dollar can mackerel or sardines is a far better bait.
As far as the antibiotics I don't buy it. At least not around here. We have between 10 or 20 head die a year here and I usually keep tabs on them for the intrest of learning. I'll share a few stories as examples.
Couple years ago in winter we had 2 cows die in an 80 acre pasture about 10 days apart. First on was treated with antibiotics twice by myself. Second no treatment. Both were dead before coyotes started on them and they started on the one I treated first and didn't start on second till the treated on was all cleaned up.
Had a horse die that we disposed of in a pasture. I spent about a hour and a half there cutting bait off the horse. Coyotes would not ever touch that horse I'm assuming because of all the human scent I left there. It just rotted away.Week or so later I dump a steer about 100yds from horse. The steer had been treated 3 times with 2 different antibiotics. It got cleaned up within a week. The horse meat I cut off for bait has probably caught somewhere in the neighborhood of 700 coyotes, so it wasn't the meat that spooked them.
One winter we had two 300 pound calves fall through the ice on a pond and drown. Pulled them out 3 days later and those coyotes would never touch those 2 calves. Only thing I can figure is maybe the smell of the muddy pond water on those calves made them coyotes spooky.
Around here coyotes are kind of weird about the odd occasional dead cow. They either clean it up or never touch it. And after watching probably over a hundred carcasses I sure can't tie it to antibiotics.
Now a deer gut pile I can leave all the human odor around it I want and it's gone the next morning.....
Another example is if coyotes won't touch a cow treated with antibiotics those feedlot dead piles wouldn't catch 20 to 50 coyotes off them every year.
Just my 2 cents from observing a few ks coyotes here.