Yes, black plums are safe for dogs.
Black Plums can be fed to your dog as long as they’ve been pre-prepared and peeled by the owner. The theory behind this is that since their skins—not seeds—are poisonous, you can remove them and feed your dog without any worries. Our house has eaten many a plum in seconds! Make sure only to give at most two or three per day, though—because too many will cause diarrhea.