That shouldn't be a problem. All it takes is another pigment in the blood that overshadows the red color of hemoglobin.
From an article:
"A group of skinks that live in New Guinea and the Solomon Islands have blood that is lime green. Now, researchers are beginning to figure out just how and why the little reptiles developed such an unusual and vibrant vital fluid.
The lizards, which are all classified in the genus Prasinohaema (meaning “green blood” in Greek), were discovered in 1969.
“The bones are green, the muscles are green, the tissues are green, the tongue and mucosal lining is green,” he says.
That’s because they are stewed in a green pigment called biliverdin. “There’s so much green pigment in the blood that it overshadows the brilliant crimson coloration of red blood cells.”
In most animals hemoglobin cells die after about four months of service. The liver then gathers them and takes out the iron, creating the green waste product biliverdin, which is later transformed further into yellow bilirubin. If too much of these toxins build up in the blood, it can cause a yellowing of the skin called jaundice. If excessive amounts of the pigments accumulate, it can be fatal.
But not for Prasinohaema lizards.
They can keep going despite having 20 times the highest concentration of biliverdin ever found in a human. And for the person, the level was fatal.
Whatever the reason why the skinks have green blood, the fact that they can survive so much biliverdin is interesting and could provide biomedical insights.
To have black blood, you just need something like a liver that works differently than in humans, which release a black pigment or substance into the blood. Or is produced by a specific gland that does nothing but producing the pigment. This would color the otherwise red blood black. The reason for releasing the black substance into the bloodstream? All I can think of is that it has certain properties regarding healing, immune system, sexual selection, a sign of vitality (a tongue that is not totally black means less pigment in the blood, and the individual could be sick or something and will not be selected as a mating partner), or it could have magical properties. There should be plenty of ideas out there to pick from.
(I also noted some anonymous member gave this thread a downvote, so I voted it back up. It really annoys me every time someone abuse the downvote function. Just mentioning it because it shouldn't hurt to point out the problem.)