Is it possible for two red dogs to produce a black puppy?

Yes due to the genetic makeup of the parents of the two red dogs. The parents could be of different colors and the black/recessive gene is still laying dormant under the dominant/red gene until future generations are born. Then, if both parents contain one copy of the recessive black allele for color, the approximately one fourth of their litter will have that black fur. So it is indeed possible for two red dogs to give birth to a black dog.

Thats all very smart, but if you think about it, who would want a red dog?