Thanks for the correction Vallie, you are correct.
Mitchel Black appears in the 1850 US Census in Cherokee Co., AL. He was 65 years old at the time placing his birth around 1765 (listed as Deleware). In his household were the children of his daughter Phebe by Ebenezer Cunningham. They were Amanda Cunningham (age 17) and John Cunningham (age 14). Also in the household was Mitchel Black's daughter Louisa age 25 (born in Tennessee). Nearby was Mitchel Black's son, John Black (John Cannon Black), age 40 (born in NC in 1810) and his wife Jane.
In 1840 Ebenezer Cunningham was listed adjacent to Mitchel Black in the 1840 US Census in Benton Co., AL.Phebe Black Cunningham, though not listed by name, appears as 20-30 years of age. This would place her birth between 1810 and 1820. Also in Mitchell Black's household were a son, age 10-15 and a daughter 15-20 (This would be Louisa b. 1825). Also in Benton County is an older John Black, age 70-80 (b. 1760-1770);an N. B. Black age 30-40 (b. 1800-1810); a James Black, age 40-50 (b. 1790-1800); a John E. Black, age 30-40 (b. 1800-1810), a Carlisle Black, a Thomas H. Black, age 30-40 (b. 1800-1810); an Alexander Black, and a James R. Black.
In 1830, Mitchel Black appears in the Pickens Co., SC Census. In his household were 3 boys under 5, 2 boys 5-10, 2 boys 10-15, his wife. No daughters. This is the same Mitchel Black that appears in the 1820 Census in Pendleton District, SC. Also, it is clear from the neighbors that he is living in the same area (part of Pendleton became Pickens). Since he was in the same area in both 1820 and 1830, it is hard to say how his daughter Louisa could have been born in 1825 in Tennessee. Perhaps he moved briefly, or perhaps she was not his daughter after all (maybe a neice or granddaughter).
It is difficult to say who Mitchel Black's father was. In 1820, he appears adjacent to a Thomas Black and a John Black in Pendleton, SC. These could also be brothers. An older John C. Black appears in the 1800 US Census in Sussex Co., Deleware. Since Mitchel Black named a son John C. Black, it is worth taking a look at this man as a possible father.
A Mitchell Black bought land in Calhoun Co., AL (this was formerly Benton County) on January 1, 1859. This is believed to have been a son of Mitchel Black.
One interesting note: This Mitchel Black's name is almost always spelled with one "L". I don't know if that means anything.