Long simmering feud among heirs is most likely reason for the blocked donation.
The reason the museum, which will open soon in Washington D.C., will not have a King display is most likely the result of disagreements within his estate.
King's children met with the curator and offered to loan the museum King's Bible and Noble Peace Prize to display but the curator turned them down. The official reason given for the decline was that the museum prefers to display gifted items, not those that are loaned and can be taken back. That is of particular concern here because King's children have a long history of feuding with each other over their father's estate.
The Bible and the Noble Peace Prize have often been a source of contention between the children.
This is another example of the consequences when the heirs of an estate cannot peaceably settle their differences. Unfortunately, in this case the entire nation has to face those consequences as visitors to the museum will not be able to see King's artifacts.
Reference: Washington Post (Sept. 11, 2016) "Why no major Martin Luther King Jr. artifacts will be at the new African American museum."