It is possible for two black Labrador retrievers to have yellow puppies if both dogs carry the yellow gene. Since the yellow color gene is recessive, both dogs need to carry it in order to have any yellow puppies in the litter.
To determine if a Labrador carries the recessive gene for yellow color, owners can send hair samples to a veterinary genetic service. This testing details all colors within a dog's genotype and outlines what color of puppies result from different adult dog matings. Test both dogs in the mating pair for the greatest chance at determining if yellow puppies may result from breeding.