It would be a government reparation, but the problem with the idea is that verification is difficult to impossible since slavery was abolished over 160 years ago. Not all Black Americans had relatives who were slaves and trying to figure out how much to pay to whom would be a logistical nightmare.
As with Native Americans, the government should acknowledge that their predecessors were wronged by the government and make every effort to avoid further discrimination, but the payment of reparations would create a lot of problems in the effort to atone for past wrongs.