Please visit
http://lgd.org
A Livestock Guardian Dog (which ever breed) will not only protect your goats from coyotes, wolves and dogs, but also mountain lions, bears and 2 legged predators.
If you have a serious coyote pack problem I recommend 2 dogs. Llamas and Burros are great agains 1 or 2 coyotes but they can't work against a pack nor are they any help with 2 legged predators.
I use dogs because their barking is usually enough to foil the element of surprise that these predators need to make a sucessful kill. If the predator does not heed the dog's warning, the dog will meet the threat head on. I like using more then one dog when there is allot of area to be protected and several head to protect. One dog moves the flock away from the threat while the other dog escalate the warning as he moves closer to the threat.
I couldn't run my farm with out my Anatolians. Do look at the above link, there is a library with information about Llivestock Guardian Dogs as well as information raising them. There are discussion groups for you when you decide to explore using them and want more personal information. I don't think one LGD breed is better then another, and if you look at the pictures at the top of the page, click on the picture it will take you to the partent clubs site that will talk about their breed. You will find one that you are drawn to. I happened to fall in love with the Anatolian Shepherd Dog, others like the Great Pyrenees. There are about 8 major breeds being used in this country and Canada.
I am sorry for your loss.