OK, based on my own earlier ideas & others, here's a brief list of potential AH conflicts the US could've been involved in over the course of the 19th C:
1819-21- USN stamps out Lafitte brothers' piracy in Barataria
1831-32- Nullification Crisis
1844-45- 54-40 Or Fight
1853-57- William Walker more successful in Nicaragua
1857- bigger Mormon War
1866-67- US intervention into Mexican CW vs Archduke Maximilian
1870- VIRGINIUS affair & earlier Spanish-American War
1871- bigger US expedition into Korea
1896- Anglo-US war over Venezuela
1898-99- bigger Samon War
Anybody think of any others ? Hmmm, a new challenge: how bout if some-1 worked on a TL somehow incorporating ALL of the above ?