In the post-American Revolution era, has the United States ever taken unilateral military action against another country besides during the Civil War?
Yes, the USA has frankly engaged in unilateral military action so many times, it would be serious work just to count them all.
Just among declared wars, three of the five (a bare majority) were one-on-one wars that the USA declared first.
Amongst non-declared wars, this has been a common scenario. Presidents Regan and Bush in the 1980's engaged in 3 of them that I can think of off the top of my head (Grenada, Panama, and the Libyan bombing).
To name just a few of the better-known instances:
1. Canada and Britain in 1812;
2. Cuba in 1898;
3. Assorted Indian Nations throughout the 19th century: Sioux, Apache, Cheyenne, etc.; and
4. Grenada in 1983;