No, the character/term appears to be something invented for the show. That said, though, there are several possibilities and we can speculate based on what we know from the comics.
In the comics, Stick is a member of The Chaste - a brotherhood of warriors based out of Japan. The primary purpose of The Chaste is to oppose The Hand - a clan of evil ninjas who worship an ancient demon. It's important to note that the final rite of becoming a member of The Hand involves drinking a potion composed of, among other things, demon blood, which transforms the subject into a state of undeath. This is, arguably, The Hand's greatest weapon, as it renders their ninjas immune to pain, fear, and often even a permanent death.
We know that The Hand will be a major player in the upcoming Iron Fist series, and that they are now officially in the MCU since
Nobu revealed himself as a warrior of The Hand, complete with their famous red uniform.
In the comics, The Hand always make it a priority to obtain artifacts or people with close ties to demonology and/or occult magic. That, along with Stick's insistence on calling the Black Sky a "thing", leads me to speculate that the weapon is actually
a human/demon hybrid. This would explain not only WHY The Hand wanted the child, but also HOW he could be a "great weapon", as well as why the child was chained the way he was inside the container. It would also explain how there could be others out there, yet be rare and/or difficult to find.
This is also supported by the fact that Japanese & Chinese mythology are supposed to play a large part in the upcoming Iron Fist series, and there were numerous other references to Iron Fist throughout the series:
The truck involved in Matt Murdock's accident had "Rand Corp" on the door, which is the company owned by Danny Rand's parents. The red dragon mark on Madame Gao's drugs is the Mark of The Steel Serpent, who is Iron Fist's primary villain.
There are also some questions regarding Madame Gao, one of the Kingpin's associates:
When fighting Daredevil, she showed superhuman strength, throwing him across the room with only a single punch. Later, she said she was returning to "her homeland", then stated that it was "much further away" than China. She may be, in fact, a demon herself, or some other mystical villain from the comics.
All of this ties together with one word: mysticism.
UPDATE: As of Season 2 of Daredevil, we now know WHY the group is looking for the Black Sky:
They want the Black Sky to lead them, and Elektra is one. It seems that her nature as a Black Sky is responsible for her inner turmoil and darkness, but we still do not know WHAT makes someone a Black Sky.