Today I played around with Ancestry to see if I could use it as a demographic tool. By searching the 1870 census using the criteria, race "colored" and birthplace "Africa," and checking the "exact" results box, I got a report of 1,690 records. I then filtered by age cohort and came up with the following numbers born in each decade:
1750-59 (16)
1760-69 (95)
1770-79 (205)
1780-89 (273)
1790-99 (309)
1800-09 (238)
1810-19 (185)
1820-29 (141)
1830-39 (81)
1840-49 (105)
1850-59 (36)
1860-69 (6)

There were also 11 "colored" persons who reported a birthplace of "Congo" and two reported born in "Benin" (in 1864 and 1867).

Someone with a good background in mortality studies could make a more sophisticated analysis of these numbers, but what jumped out at me was the dramatic downward trend in numbers of persons in each age cohort born after 1800, indicating the effectiveness of the US ban on the African slave imports imposed in 1808.

It is impossible to tell from the census whether any of these African-born persons were NOT ex-slaves; I assume if any were free-born immigrants, their number was fairly small. I noticed in south Florida many of these African-born persons have Spanish names, suggesting that they may have immigrated from the Caribbean or possibly from South America after Emancipation.

Certainly we can question the accuracy of the 1870 census data (did the enumerators always ask birthplace, or were some too lazy and just assumed a local birthplace?). The pirate-slaver Wanderer, on its one-and-only slave voyage, landed 325 Africans at Jekyll Island on the Georgia coast on 1 December 1859 -- these persons, presumably in the prime of life, would only have aged 11 years by 1870. Unless we believe that the Wanderer's human cargo constituted virtually the entire illegal trade in the 1850s, we can guess that the census undercounts African natives. On the other hand, even if wildly under-counted, these census numbers do not support the idea of a huge illegal African slave trade to the US.

Other interesting things I found playing with Ancestry:
There were 40 African-Americans in 1870 with the given name "Africa" and 15 persons with the surname "Africa."
There were several hundred white African natives -- mainly from South Africa -- living in the US by 1870.
The 1880 census enumerated 929 non-whites born in Africa or Congo (26 of them born after 1860)
The 1900 census showed 472 natives of Africa, including 2 Senegalese living in Hawaii -- but by the time of this census, the majority of Africans were immigrants born after the 1865 Emancipation.