Some dogs' strong natural predatory instinct can pose a real problem when you start introducing them to livestock such as goats. Dogs naturally have a desire to chase other animals; their instinct is to subdue if not kill and eat. A proper introduction with adequate training will be necessary to keep all of your animals safe during the acclimation process. Pay careful attention to your individual animals and know that some dogs may accept goats more willingly than others.
Place goats in a fenced enclosure that your dogs cannot get into. Allow the goats to become acclimated to the environment. Allow your dogs to see the goats through the fence and gauge their behaviors. Pay attention to which dogs growl at the goats, which seem afraid of the goats, and whether any want to chase the goats while separated by the fence. Verbally reprimand your dogs for any behaviors they display that you find objectionable, such as growling or trying to chase the goats. Of course, if you haven't undertaken basic obedience training already, commit to it immediately. Move on to Step 2 when the animals no longer seem to pay significant attention to one another through the fence.
Allow your dogs to enter the goat enclosure under your supervision. Place your large dog kennels inside the larger goat enclosure, then guide the dogs on-leash into the kennels. Allow the two species to sniff at one another and interact while separated by the kennel. Continue doing this for several hours each day until the animals have comfortably accepted one another.
Walk your dogs through the goat enclosure on a leash, one at a time. Place a muzzle on any dog you believe might behave aggressively toward the goats in any way. Walk your dog on-leash inside the goat enclosure until you are certain your dog has accepted the goats and will behave in a manner you find acceptable, then release the dog from the leash. Closely supervise your dog with your goats until you are sure they're in a contentedly coexistent state. If one dog doesn't acclimate in a session, kennel him and move on to another dog. Ultimately you'll know which dogs will cohabit with goats and which you'll have to supervise or segregate.