Your challenge is to establish a Bonapartist monarchy in any country of the Americas. This must be a locally ruled. Preferably, there should be no Bonapartist states in Europe.
1: There were schemes after Napoleon was exiled to get him off Saint Helena and have him take over leadership of revolutionaries in South America in Pernambuco, Brazil, or exiled French Grand Armee soldiers in Texas.
2: Napoleon's initial coup against the Directory fails and he flees and takes over Louisiana.
3: The American Revolution and early history of the nation is influenced by pro French elements like Jefferson and the Jacobin societies and the XYZ affair and the Quasi War never happen. Having a Bonaparte style imperial presidency becomes popular and leads to Aaron Burr seeking to emulate Napoleon...
1907: Some catastrophe wipes out the President, Vice-President, and Secretaries of State, War, and the Treasury of the United States. The Attorney General accedes and rules by decree "for the duration of the crisis". He grows more and more paranoid and insane, eventually proclaiming a monarchy shortly before his ouster.