First black comic-book main character
This honour goes to "Lion Man", who debuted in 1945 as the hero of the groundbreaking one-shot "All Negro Comics #1". While he doesn't have any discernible 'lion powers' he does seem to have exceptional agility, hearing and aggression. He's heroic, but not superheroic.
First (regular) black character in a superheroic comic
This honour goes to Gabriel "Gabe" Jones, debuted in 1963 as one of the Howling Commandoes. Although he doesn't have any obvious superpowers, it's notable that he doesn't age, something that has been commented upon in-universe (with regard to Nick Fury).
First Black title superhero with powers
This would probably be T'Challa, otherwise known as the Black Panther, who debuted in 1966 in Fantastic Four #52.
His powers include...
...superhumanly acute senses and increases his strength, speed, stamina,
reflexes, and agility to Olympic-levels. He has since lost this
connection and forged a new one with another unknown Panther deity,
granting him augmented physical attributes as well as a resistance to
magic. His senses are so powerful that he can pick up a prey's
scent and memorize tens of thousands of individual ones. Following his
war with Doom, T'Challa loses his enhanced abilities only to once
again establish a connection with the Panther God.
which leads us to the...
First Superheroic black character
As pointed out by Omegacron in his comment below, the first superheroically powered black character is "Lothar", Mandrake the Magician's sidekick who briefly debuts in the first Mandrake story in 1934. Lothar is described as the "Strongest Man in the World" and on at least one occasion lifts an elephant into the air, a feat that goes well beyond normal human abilities.