My impression is that such a period of time would be rather short. Even though the US has only officially declared war 5 times, its military has been continually involved in operations around the world from quite early on in the history of the nation.
Alternatively, what period of history was considered the least active for the US military?
Depends how you define it. If you want to count every U.S military operation ever I don't believe a year ever went by where the American military wasn't doing something.
What counts as a "conflict"? There are dozens upon dozens of little excursions the military went on during the United States' age of Imperialism but are they all conflicts? Does Mathew Perry's "Opening of Japan" count as a conflict? We have to limit our parameters here.