I watched a pair of donkey's protect a flock of chickens once.
One of the donkey's went after the coyote and the other stood by the chickens to protect them.
Its wise to get 2 donkeys.Sometimes, even in a small field, a single guard animal can be overwhelmed.
Donkeys are extremely intelligent, with acute hearing (there is a reason for those big ears) and sight, and they are conservative by nature: they do not like change in their surroundings, and will drive off a coyote or stray dog as much because it is an intruder as from any instinctive dislike of canines.
If you're shopping for a guard donkey, stay away from intact (stallion) jacks in favor of a gelded jack or a jenny (female). Some breeders test and/or train donkeys for guard duty and will sell them with an agreement that will allow you to exchange the donkey for another if it doesn't work out as a guard. Remember too that a jenny with a foal may be too busy to watch a flock. Even a jenny in season is thinking more about jacks than about coyote
Donkeys are easy to care for good grazing or hay and water is all they need and delightful barnyard pets, if you accept that they are clever and rigid.
And yes even mini donkey's can be used.