Born in New York City, Alvin was one of three children to Elizabeth Miller, daughter of Nathan L. Miller, and Alvin P. Adams Sr. His father was a Western Airlines executive.
His mother owned a bookstore. The younger Adams attended Yale, like his father, and received a J.D. from Vanderbilt University Law School.
Alvin was appointed as the United States Ambassador to Djibouti in 1983 and served until 1985.
His next ambassadorship was in Haiti, where he convinced Prosper Avril to relinquish power in a late night conversation held in March 1990.
In 1992, Adams was named ambassador to Peru, serving in that post until his retirement from the Foreign Service in 1996.
Alvin also worked in Washington, D.C. for what became the Bureau of Counterterrorism and was posted in Vietnam, where he met his wife, Mai-Anh Nguyen.
They had two sons, Lex and Tung Thanh, who died in the 1989 USS Iowa turret explosion.
Alvin moved to Portland, Oregon in 2011, where he died on October 10, 2015, aged 73.