Yeah, I know it's near impossible but that's why it's a challenge! Maybe some far thinking segragationist decided that premptively gerrymandering the Black population by coming as close as possible to forcing the move?
I'll take a stab at it but statehood doesn't come until way after 1900....
Congress takes an interest in the American Colonization Society's project and grants it a formal charter to annex territory in Africa on behalf of the United States.
In 1821, Cape Mesurado Territory is formed on land bought from the indigenous King Peter.
In 1824, the name is changed to Liberia Territory and a capital is built. It is named Monrovia after President James Monroe.
ITTL, Liberia Territory attracts more colonists as a formal territory of the US. It never declares independence, and has a population of over 100,000 Americo-Liberians by 1870, as many freedmen after the American Civil War decide it's safer to go back to Africa. The reversal of Reconstruction in the former Confederacy brings a huge wave of settlers into the 1880s and 1890s.
Liberia Territory receives mostly benign neglect from the US, being allowed to elect its own local officials but having no representation in Congress.
World War II brings renewed American interest in Liberia Territory as a base of operations for a northward thrust into Europe. After the war, the Civil Rights Movement in the US and the granting of statehood to Alaska and Hawaii put the issue of statehood for Liberia forward as a symbolic issue of racial equality. The State of Liberia is proclaimed on July 4, 1967.