Veterinarians don't recommend giving cow's milk to dogs, as it can cause diarrhea. Newborn puppies can drink their mother's milk. If puppies do not have access to their mother's milk, the owner can provide a commercial canine milk substitute formulated for puppies, according to the ASPCA.
Along with diarrhea, dogs can experience an allergic reaction in the form of itchiness from consuming dairy-based products, states WebMD. Other beverages to avoid giving dogs include tea, coffee and alcohol. Foods that dogs should not eat include chocolate, raisins and macadamia nuts. A dog owner can contact the ASPCA Poison Control Center at 888-426-4435 to find out what to do if his dog eats something unsafe, as of June 2015.