keeping a farm dog while im gone?

Are there people at the farm on a regular basis? If not, then you really shouldn't get a dog. Dogs are very emotional animals and if you want it to be a good dog, then they need constant interaction with you. If they don't see you on a daily basis, they can't learn to trust you, so they won't obey you. I would suggest that if you get a dog, you need to at least make it an option to have the dog travel to and from the farm with you.

If you insist on having a dog, when there are not people around regularly, you will need to keep it penned up. If you have a coyote/stray dog problem, when human's aren't around, they will need the protection that a pen provides to keep them safe.

If there are people at the farm on a regular, constant basis, once the dog is trained, it will probably do it some good to be out and about instead of penned up all the time.

Some good breeds for farms/cattle include:

Australian Cattle Dog, Border Collie, Blue Heeler, Belgian Sheepdog, Bernese Mountain Dog, Old English Sheepdog, etc.

Only have a dog at your home! Then you can take it to the farm. It sound like that you aren't ready for a dog. It's selfish to make a dog stay there, so you can have it for fun. It would probably get hurt by the coyotes if left alone.

Find a human -not a dog!

Look into Great Pyrenees, they're bred to be outside dogs and to protect sheep. I would personally not leave my dog free roaming while I'm not at home and all dogs, even independent pyrs need a family and attention. Have you considered electric fencing? Wireless electric fences allow dogs to roam a certain distance from the transmitter in any direction, but gives them a warning when they go to far, and eventually, a shock if they go further than the preset distance. Dogs, especially working dogs, seem to catch onto and learn the boundaries pretty quickly. Pyrs are very independent and are bred to live with their livestock. And they're huge dogs- easily more than 45lbs, closer to 100. Still, they need companionship and no dog should be left outside, unattended, overnight or longer. Good Luck!

I wouldn't consider leaving a dog either penned or free roaming for two or three days alone as you describe. It's not unknown for dogs to leave such conditions and go feral.

Get a friend with a really large shotgun. Coyotes aren't on the endangered species list.

a concrete statue of a dog is the only thing I could think of that could take 3 days of neglect

you should ask a friend to watch it.

i don't actually know about it