The federal government was behind most of the advances in African American rights during the time you mention. The government often needed to be pushed by activists, but it was much more in favor of black rights than the states were.
For example, it was the federal government that pushed for black rights during Reconstruction. This was how the 13th, 14th, and 15th Amendments got passed, giving blacks the right to vote and the (official) right to be treated equally.
Later on, after WWII, the federal government needed to be pushed, but eventually helped with civil rights. It was the federal government that forced Arkansas to allow the Little Rock Nine to integrate Central High. It was the federal government that passed the 1964 Civil Rights Act and the 1965 Voting Rights Act.
In short, though the federal government has not always been very eager to push black rights, it has done much more than state governments did. All of the major black rights victories have come through the federal government.