I'll sketch the history of Liberia to 1860 out; the idea of resettling freed American slaves in Africa had its seed in the 1787 establishment of the British colony at Freetown, in what is now Sierra Leone. In 1817, the American Colonization Society was founded; this group was an alliance of free blacks and whites that supported colonization. Some white supporters genuinely wanted black people to have full freedom and equality; others wanted black people to be removed from America entirely, or at least free black people.

The first 88 emigrants arrived in West Africa in 1820, looking for land to settle on. They got little help from British authorities and open hostility from local tribes. The next year, the emigrants sailed south to meet with representatives of tribes living near what is now Monrovia. The local tribes were hostile to new settlers, especially those that threatened their lucrative part in the slave trade, and the deal they signed to grant the settlers a strip of coastal territory (about 100 square miles for $300 in trade goods) was literally signed at gunpoint.

The ACS colony was governed from the small town of Christopolis by the white missionary Jehudi Ashmun, and many settlers chafed under his rule, which was sometimes arbitrary and always harshly authoritarian. Several of the black settlers forced him to leave the colony. The ACS sent a representative to negotiate a settlement; Ashmun returned, bound by a constitution and a code of laws, and the black settlers accepted his authority - out of necessity, as they were absolutely dependent on the ACS for trade goods and a flow of new settlers.

Of the 4,600 settlers who landed at Christopolis (now renamed Monrovia) over the next 20 years, fewer than half survived. Disease was rampant, and the six American colonies in the region faced constant conflict with the indigenous nations. Many of the tribes in the area were relatively recent arrivals, and Liberia was contested between them; it was only the diplomatic intervention of other regional powers, and the British at Sierra Leone, that preserved the fragile settlements. The nearby presence of the U.S. Navy's small Africa Squadron prevented the Liberians from losing their control of the coast, and control over the coastal trade was a vital advantage.

Even with this support, the "black white men" fought several wars before four of the six colonies coalesced into Liberia in 1841; one was destroyed, and the sixth colony remained under the direct control of the Maryland Colonization Society. Liberia, now under the governance of the black Governor Joseph Jenkins Roberts, declared its independence in 1847 after British traders refused to pay tariffs to the ACS, a private organization. Maryland's colony declared its independence in 1853, but the struggling nation of Maryland in Africa joined Liberia in 1856.

The new Republic of Liberia needed resources desperately, but the most important was manpower. President Roberts had appealed to the U.S. Congress to provide money and weapons so the Liberians could consolidate their control over the coast and end the slave trade in the region, thus fulfilling an important moral mission for Liberia while also breaking the power of the inland tribes, but Congress refused. Congress did direct the U.S. Navy to reinforce the Africa Squadron and turn over any slaves they confiscated to the American Colonization Society, which was still sending settlers and material support to Liberia. In the last year before the Civil War, 4,500 former slaves were resettled in Liberia. The "Americo-Liberians" were still a small minority in the land they claimed, numbering perhaps 15,000 at that time against a half-million indigenous Liberians (and they remain a small minority today, about 5 percent of Liberia's population).

News of the Civil War sent a shockwave through Liberia. The Navy withdrew the Africa Squadron. This had little effect on Liberia, since Britain's Royal Navy had a much larger presence in the region and was much more effective at anti-slavery patrols.

Dramatic changes soon came; in September 1862, the United States (after approval by a Congress largely emptied of Southern votes) formally recognized the Republic of Liberia, and signed a trade agreement the following month - but not before President Lincoln had floated, in a meeting with two black ministers, the idea of removing all black people from America entirely, resettling them in Liberia and/or Central America. When reports of the meeting were published, they met swift condemnation from black leaders such as Frederick Douglass and white leaders such as Salmon Chase. Given the private nature of the meeting, Lincoln was quickly able to declare he'd been misunderstood - but by the time the Emancipation Proclamation was announced a few months later, the alternative of deporting all black Americans had already been discussed and dismissed. It's very possible this was Lincoln's intent in the first place.

During the war, Liberia was largely consumed with the work of consolidating its control. Fighting a series of guerrilla wars against the indigenous peoples, and gaining a workforce for its fledgling export economy, was the nation's overriding concern. Large villages were set up for "Receptive Africans," mainly those uprooted by the constant state of low-grade war along Liberia's encroaching inland borders. They received instruction in Christianity, the English language, and the art of backbreaking labor to grow sugar and cacao for export.

Liberia's population, of course, followed the Civil War with great interest, but mostly and correctly in self-interested terms. Liberia was delighted to receive an American consul in 1864, and to send an ambassador to the black Republic of Haiti, but it was most interested in gaining the revenues to pay off its debts and expand its infrastructure - and that meant gaining a "civilized" population capable of overwhelming the "aborigines." The Emancipation Proclamation seemed to hold out the hope of an America which would recognize black equality - and this was ironically a serious blow to Liberia. As Liberia's President Daniel Bashiel Warner told Liberia's Congress in December 1865:

Our need of population is immediate and urgent. Our immense resources cannot be developed... simply for the want of minds and hands to engage in the necessary operations.

...We have again and again invited our brethren in the United States to come over and help us fill up the vast solitudes, which for centuries have remained uninhabited... My confidence remains unshaken in the destiny of Liberia. She is yet to be the asylum of the oppressed American negro and a beacon for the guidance of the benighted tribes of this continent.

After the Civil War, black Americans did emigrate to Liberia, but in small numbers; of the almost five million black people in America, fewer than a thousand set sail for Liberia in 1866. Not even the collapse of Reconstruction could spur more than a few hundred black Americans to seek refuge in Africa; Haiti and Canada remained the most popular destinations for black emigrants.

Sources:

Another America: The Story of Liberia and the Former Slaves Who Ruled It by James Ciment

The Annual Messages of the Presidents of Liberia 1848–2010: State of the Nation Addresses to the National Legislature edited by D.Elwood Dunn