Blackberries are okay for dogs to eat in moderation, though they should be fed more traditional dog food on a regular basis.
Unless your dog has some rare food allergy to these berries, you shouldn’t have to worry about causing them any health problems as a result of giving them blackberries.
There are lots of dogs and even foxes that eat these berries on a regular basis and do not get sick or experience any health problems at all. As long as you limit giving them blackberries to just once in a while, your dog should not have any issues whatsoever.