There are a few things that you can try that would be safe. Believe it or not good old fashioned peanut butter had helped to remove tar and other things from the fur. Mineral oil is safe and that can be used as well. Vaseline may help also.
As a last alternative you can cut the fur out in the areas where the sap is or take the dog to a professional groomer.
You may have to work with it and use the products repeatedly until the stickiness is gone. Basically anything that is oil based and is safe for dogs should help to remove the sap. I have actually used skin so soft cream from Avon for many of my great danes fur issues. Depending on the area of the sap you have to be careful so that the dog won't lick the product if it is not proven safe. I don't know how safe skin so soft is but I would be very weary of giving my pet a treatment of something that can remove rust from wire cages and bath tub stains.
I hope you are able to get the sap off. I would personally try peanut butter first as it is 100% safe, unless of course your dog happens to have an allergy to peanuts.
Good luck and if you have any further questions please feel free to ask.
Sincerely,
Bunny
Veterinary Assistant
10+ years at a veterinary clinic as a veterinary assistant. 20+ years raising/showing rabbits