no a pig would probably kill the goat. Get another goat would be the best option. Or even a sheep. With a sheep you can have the wool to spin and make into something. Sheep and goats go together much better than pigs and goats.
It depends on the dog. Some dogs will help keep the coyotes away but others won't ( if you have a specific Guardian type dog Ie German shephard, or other guard type dog, those are better then the run of the mill mut) And you need a dog the same size or bigger then the coyotes also. You don't want to have your basset hound match wits with a coyote.