Here's my time line for it, including a set of poorly done maps.

Red is loyalist controlled territory. Blue is USA.
April 12, 1980- William R. Tolbert Jr, president of Liberia, decides to make a surprise appearance at a local playhouse. The attempted military coup, which featured a night raid on his mansion home, fails to capture him. William flees to a secret location.
April 13, 1980- With Tolbert having seemingly fled the coup is declared successful and Samuel Kanyon Doe is declared the new president of Liberia.
April 21, 1980- Tolbert reemerges along with a loyal portion of the army. In his 'Loyalist Uprising' Tolbert's forces seize the Southern portion of Liberia, including the cities of Nyaake and Harper
April & May 1980- Following the surprise attack the Loyalists gain the upper hand, they make some small gains moving directly North along the coast, nearly reaching Greensville, as well as to the East, shielded by the Putu mountain range.
June-August 1980- The Rebels, aka the supporters of the military coup, launch a counter offensive, driving loyalist troops away from Greenville and forcing them east. By this time it has become clear that the loyalists are heavily outnumbered.
September 1980- The rebels surprise the loyalists by launching the 'September Offensive' retaking the loyalist gains east of the Putu range.
October 1980- The rebel advance is slowed to a grinding halt just north of Nyaake. The loyalists heavily entrench themselves. William R. Tolbert Jr, having increased good relations with the Eastern bloc begins speaking to Warsaw members asking them for support.
November & December 1980- The Soviets, hoping to secure an new ally in Africa, begin shipping arms to the loyalists. With the Soviet help the loyalists are able to withstand any further advances. Tolbert appeals to the Soviets to send troops but the Soviet Union refuses, citing the distance between the two as their reason.
January 22, 1981- Stunning many people around the world, in his first major action as president Reagen sends troops in to aid to loyalists, whom he feared would turn into soviet allies if they won. They land in a surprise assault, taking the capital of Monrovia.
February 28 1981- By this time the USA has secured much of the land around the capital, forcing the rebels into a true two front war. The loyalists are also able to make advances with the rebels distracted.
March-June 1981- Loyalists and USA continue to advance, with the rebels unable to stop them. The rebels are on the verge of collapse.
July 7, 1981- Samuel Kanyon Doe is overthrown by his military, which then proceeds to surrender, ending the brief Liberian civil war.
September 5, 1981- The Liberian government, feeling it had secured the country, requests US troops to leave, they do so. A new high has been reached in relations between the two countries and Liberia seems to have been secured as a permanent US ally.
November 18, 1981- A series of terrorist car bombings rip through Monrovia. Hundreds are killed. A group calling itself the Liberian Liberation Army (LLA) claims responsibility. President Tolbert claims it to be an isolated assault.
January 1, 1982- New Years celebrations across Liberia become the new target of the LLA, who kill many innocent civilians in their attacks.
February-May 1982- The attacks become more and more common as the LLA gains support and momentum. Tolbert grows increasingly unpopular.
June 6, 1982- Tolbert is impeached, the country falls onto the verge of civil war. Attacks break out across the country and many fear a renewal of the war, after such a short peace.
June 11, 1982- At the request of the acting government of Liberia US troops return to secure the situation. It is clear by this point that Liberia is entirely dependent on the USA.
July 2, 1982- Work begins on establishing an independent government in Liberia.
August 14, 1982- Reagen announces, famously, that the talks are over. A new government is established in Liberia, but US troops remain.
August-December 1982- The new government grows increasingly unpopular due to infighting and continued reliance upon the United States.
February 9, 1983- The government of Liberia collapses, the country again falls to the verge of civil war and again it is only the USA that keeps it from happening.
February 15, 1983- Realizing that a independent government is entirely impossible at this point, Reagen and the leaders of Liberia announce Liberia is to become a protectorate of the USA.
February-December 1983- The USA does much work to improve Liberia and they become relatively popular among the citizens of the USA.
January 1984-May 1984- As the USA gets in full election swing the USA continues work in Liberia, although to a slightly smaller degree.
June 1984- Realizing that they are behind in the polls Democrats begin attacking Reagen on the issue of Liberia, calling him a dictator and claiming he is illegally occupying the country against the will of the majority.
July-August 1984- The issue reaches a crisis point, threatening to cause Reagen to loose his bid for reelection. Thus Reagen announces that there will be a referendum in Liberia over the issue on election day. The choices were to be independent, current status, or to become a US state.
November 4, 1984- Reagen solidly wins reelection. In Liberia, though, the vote is a stunner. It seems that pro-US supporters had united behind statehood. The final referendum stood at: Independence 40%, Remain as Protectorate 9%, Become US State 51%
51 star US flag adopted after Liberia joins USA.