On April 2, 1956, US President Dwight David Eisenhower signed into law a bill that established the Booker T. Washington National Monument (Public Law 84-464). The new law transferred ownership of the BTW Birthplace Memorial to the US Government and placed it under the authority of the Department of the Interior; it took a bit more than a year for the full transfer to take place. Sidney J. Phillips, the man who was the founder of the Birthplace Memorial and who had served as the President of the Booker T. Washington Birthplace Memorial since its creation in 1946, was no longer to be in charge once the Department of the Interior took over.
Though his Birthplace Memorial management days were soon to be behind him, Phillips was not ready to say "Goodbye!" to Booker T. events or to sponsoring US commemorative coins.
I've written before about the efforts by Phillips and the Booker T. Washington Birthplace Memorial to secure a 1956 half dollar to help mark the centennial of BTW's birth. (See link below.) Between March and June 1956, three separate bills were introduced in the House of Representatives proposing such a coin. As the transition of the Birthplace Memorial to the US Government was pending, the three coin bills named the Booker T. Washington National Monument Foundation as the sponsor/beneficiary vs. the BTW Birthplace Memorial; net funds from coin sales were to be used to defray expenses related to BTW Centennial .
The bills were all unsuccessful, however, each failing to be reported out by the House Committee on Banking and Currency to which they had been referred. In July 1956, a different tact was taken - a request for commemorative medals. Brent Spence (D-KY) introduced a bill in the House that sought the striking of 10,000 medals "in commemoration of the one hundredth anniversary of the birth of the late educator, Booker T. Washington.
The sponsor/beneficiary of the medals was to be the Booker T. Washington Centennial Commission - Sidney J. Phillips - former President of the Birthplace Memorial organization - was President (or Executive Director - I've seen both titles used) of the newly established Centennial Commission.
As with the previous coin bills, the medal bill was referred to the House Committee on Banking and Currency. Also like the previous coin bills, the medal bill was not reported out by the Committee and thus failed to be approved. The days of US Mint-struck commemorative coins/medals honoring Booker T. Washington were officially over.
My searches thus far have not turned up a privately-struck BTW Centennial medal. The US Post Office Department did, however, issue a 1956 BTW Birth Centennial stamp, so the milestone was not completely bypassed by the US Government.
Concluding Note: Though it did not secure a coin or medal from Congress, the Centennial Commission did secure an appropriation capped at $225,000: "For necessary expenses of the Booker T. Washington Centennial Commission to carry out the year-long celebration of the one hundredth anniversary of the birth of Booker T. Washington and to promote the spirit of interracial good will, and revive interest in the practical policies, programs, principles, and philosophies of Booker T. Washington." (The controversy regarding the Commission's potential misuse of these funds is worrisome. but beyond the scope of the present discussion.)1956 Booker T. Washington Birth Centennial Stamp
1946 Booker T. Washington Half Dollar

For more on the Proposed BTW Centennial coins, see:
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What If? 1956 Booker T Washington Coin #3For more of my topics on commemorative coins and medals, including more on the history and design of the Booker T. Washington half dollar, see:
Commems Collection.