The history of COs in the United States of America goes back to the founding of the country.  In fact, the pilgrams and others who first came from Europe did so in part due to their conscientious objection to the fighting in England and Europe.

On July 18, 1775 one of the first laws passed by the Continental Congress exempted conscientious objectors from military duty.

During the discussions among the Founding Fathers regarding the Second Amendment and the right to bear arms, the question was raised whether or not the right not to bear arms should also be included.  They decided that the right not to bear arms was so basic that it did not need to be included in the Constitution. In this case they failed to foresee that later generations would see it differently. 

Here are some brief notes on the History of Conscientious Objection from PBS.

History of Conscientious Objection in the United States

Colonial Age
In the colonial age of America, the right to religious freedom was often expressed as the right of an individual to his or her own conscience. This freedom, which was recognized in many of the colonies — and eventually by the first amendment to the Constitution — shielded many religious sects, including pacifist groups such as the Quakers.

Near the beginning of the American Revolution, George Washington called for a draft to fill the ranks of the Continental Army, exempting "those with conscientious scruples against war."

Civil War
During the Civil War, the first federally mandated draft in the United States was implemented, and instances of cruel punishment and deaths of conscientious objectors were first recorded, including being starved and hung by their thumbs.

World War I
World War I saw the reinstitution of the draft at the same time that popular opinion was divided over American participation in the war. Government prosecution of conscientious objectors was intense, and resisting conscription or encouraging others to resist conscription led to arrest and imprisonment for many Americans. Of the 450 conscientious objectors found guilty at military hearings during World War I, 17 were sentenced to death, 142 received life sentences and 73 received 20-year prison terms. Only 15 were sentenced to three years or less.

World War II
In the time leading up to World War II, President Franklin D. Roosevelt implemented the Selective Service and Training Act of 1940, which was the first peacetime draft in United States history. This period was also marked by the government's recognition that some would oppose military service for religious or conscientious reasons. During World War II, there were 34.5 million men who registered for the draft. Of those, 72,354 applied for conscientious objector status. Of those conscientious objectors, 25,000 served in noncombatant roles, and there were 12,000 men who chose to perform alternative service.

Those who chose alternative service worked in Civilian Public Service camps. These service camps were operated by religious groups, including churches rooted in the pacifist tradition, such as the Mennonites and the Quakers. These camps predominantly put men to work on improving soil conservation or preserving state and national parks.

Vietnam War
The Vietnam War, which became a flashpoint for controversy in the 1960s and 1970s, provoked many more individuals to claim conscientious objector status. Over the duration of the conflict, the Selective Service recognized 171,000 conscientious objectors; 3,275 soldiers received discharges for conscientious objector status that developed after their induction into the military. In addition, hundreds of thousands of men, many of whom were conscientious objectors, avoided the draft by leaving the country or refusing to register.

The Gulf War and the Wars in Afghanistan and Iraq
After the end of the draft in 1973, the military became an all-volunteer force. Before the 1991 Gulf War, 2,500 men and women refused to serve based on conscience. Eventually, 111 members of the Army were officially recognized as conscientious objectors.

During the wars in Afghanistan and Iraq, far fewer soldiers have made it through the process to become conscientious objectors. In 2006, the Army reported only 42 applications, of which 33 were approved. Advocates and outside observers have argued that these numbers are artificially low because they reflect only those soldiers who complete the lengthy application process. According to the Center on Conscience and War, they received one to two calls per month to their GI Rights Hotline in 2000 and 2001 from someone in the military raising questions of conscience. By 2002 and 2003, they were receiving at least one to two such calls per day.

The conflicts in Afghanistan and Iraq have been the occasion for a growing number of desertions — defined by the military as soldiers absent without leave for more than 30 days. In 2006, the Army reported 3,196 desertions, a sharp increase from two years earlier, which saw 2,357 desertions. At the same time, the number of prosecutions for desertion went up, a move described by military lawyers as an effort to discourage soldiers from leaving their assignments.