It seems everywhere you look, the US has played host to a number of conflicts. The sad part is that most everyone doesn't know about them - they're forgotten to general public knowledge. The sadder part is that we gloss over some of the most colorful parts of American history to reenact. The Pig War is a prime example. It wasn't a big conflict, it was bloodless, but it's interesting nevertheless.
The Fenian Raids are an almost forgotten piece of history. Ever watch the movie Canadian Bacon? Not so inconceivable, at least in 1866 and in 1870. After the American Civil War, Irish veterans from the Union army conducted a series of raids into Canada. These are reenacted events, and have interesting pages detailing the history.
The Toledo War of 1835-36 is another very forgotten piece of history. I only found out about it last night watching a show about the Michigan and Ohio football rivalry. But if you look at the historical conflict, it would make a great fun reenactment. I think it has been reenacted in the past, and I think there is a push to do so again.
Shay's Rebellion in 1787 would also fit into this category, although it probably gets more educational play than most of the other small forgotten conflicts. John Fries Rebellion of 1798, though lesser known, would be nice reenactment material along the same lines as Shay's Rebellion.
So, if you're having the blues reenacting the big wars, do some research and see what you come up with close to home as far a small forgotten conflict. You might be surprised at what you find.