Best way to take out some coyotes?

Putting a major dent in the yote population is tough if you neighbors do not help. I would just set up with a game caller and a rabbit tail bait.
Start shooting as often as you can. At the very least, they may stay away from your property for a while

.17HMR

You will probably get a response about soaking sponges in baking grease or soaking hotdogs in antifreeze - dont do that

If you have a fenceline on the property, you can find where they are going under and set up a snare, otherwise trapping blind is pretty tough. You can also try and do some calling or night hunting for them. Success can be very limited. They either come in real quick or dont come in at all

Also, coyotes have compensatory reproduction so if you do go out and shoot a bunch this year, they will make up for their losses by producing multiple litters the next year.

Go get em

Like many have said, trapping is tough. I'm about to order some new ones and start giving it hell. You pretty much have to catch every possum in the area and get them out the way first cause they will be in the trap on the first night it's set

i have yet to see where they have had adverse affect on deer.. primary diet is rodents

Crows, armadillos, hawks, ratsnakes, owls, etc. All will take out eggs or a turkey