After reading the responses to my question about Libera being a US territory, I thought I would give my five cents to this discussion.
Since Liberia was created for freed blacks, there may be laws to limit if not discourage whites from moving to that territory. The initial political system would likely be a territorial governor appointed by the President and a territorial legislature elected by the residents of Liberia. In the beginning, the governors would be white and from the continental US. Other than the governor and his staff, the white presence would probably be limited to a couple of Army forts, naval ships and essential industry.
After Liberia established itself as a country in OTL, the True Whig Party emerged as the dominant and literally, the only legal political party (the True Whigs won every presidential election from 1878 until William Tolbert was overthrown and executed in 1980 by the Liberian armed forces).
I believe that the dominant party in Liberia would be the Whigs until the late 1850s. No way would Americo-Liberians support Democrats as they were dominated by slave owners and Southern (secessionist) politicians.
When the Civil War begins, many Liberian men would want to fight in the Union army in whatever roles would be appropriate for them.
During Reconstruction, the Radical Republicans dominating Congress may push for minor changes in Liberia's political system, such as appointing a (black) resident of Liberia to the governorship and allowing the election of nonvoting delegates to the US House of Representatives.
There would still be institutional discrimation by the Americo-Liberians against the indigenous population as in OTL (for example: forcing them to sit in the back pews in church, banning them from Masonic temples, forbid marriages between the two groups).
When Liberians hear stories about segregation and Jim Crow laws in the south, moves may be made to give the vote to all residents of the territory (and ensure Republican party dominance in Liberia).
If Theodore Roosevelt become President, he might have the law changed so that Liberians can elect their own governors (changing status from territory to commonwealth, just like Puerto Rico and the US Virgin Islands). When Roosevelt leaves office and embarks on his hunting trip to Africa, he may add Liberia to his itinerary.
In OTL, most Americo-Liberians had jobs in government (either elected office or patronage positions) and very few of them owned their own businesses. A lot of mom and pop stores in Monrovia were owned by Lebanese families who hired the indigenous blacks. Liberia's armed forces were dominated by the indigenous blacks. It is no surprise when the military had enough in 1980, stormed William Tolbert's presidential mansion, and brutally murdered him).
With FDR in the White House, Liberia would be a recipient of the New Deal. Public works programs would lead to the development of infrastructure and a modern highway system. When the US enters World War II, the member of Liberia's various ethnic groups would enlist en masse. In OTL, black Americans switched their political loyalties to the Democrats. So would the Liberians ITTL.
We might see a middle class emerge from the various tribes that would shift political control from the Americo-Liberians by the 1950s or 1960s. Multiple political parties would result, e.g. Democrats, Republicans, Socialists, pro-statehood, independence, pro-commonwealth.
Monrovia emerges as a popular tourist destination and port of call for many cruise ships instead of being mired in riots, child soldiers and lack of electricity.
