The Kenyan and Nigerians at our church, who have become American citizens, just call themselves American.
They do not understand American born blacks.
If someone is born elsewhere, NOT of American parents, then that person is not considered "whatever"-American, because they're not of American birth. My Grandparents were of Italian descent, but they weren't born in Italy, THEIR parents were. Since they were the first generation born in American, they probably called themselves Italian-American, but I wouldn't consider myself as such, because being one generation removed, I'm a blend of the Italian-Irish of my Mama, and the Scots-Irish-Cherokee of my Daddy. So I'm just a Heinz 57, and have several ethnic groups with whom to celebrate. ;o)
I've had friends who had moved from Africa, both Uganda and Kenya, but I don't think they consider themselves African-American, they're just African. Since their kids were born here, they'd be considered African-American.