Depends on what you define as a conflict.

If you only count the American Revolution, War of 1812, Mexican American War, Civil War, Spanish American War, WW1, WW2, Korean War, Vietnam War, Persian Gulf War, and War on Terror, then there are several years that the US has been as "peace".

However, we often forget the most persistent and defining conflicts of the US, the Indian War. On and off, the US has consistently been at was one with Native American tribe or another since 1776 (or even).

You can arguably classify Indian Wars as lasting from 1776 to 1900. After that, the US has intervene in Latin American countries several times and engaged in occupations.

I don't think it is possible to find a single year in US history when American soldier were not deployed to fight in some sort of conflict. If anyone where is such one, I'm sure I can find a conflict that the US armed forces were involved in at the time.