Would it be possible for the government of the Confederate States of America to flee the mainland of North America and establish a regime in exile, sort of like the Republic of China IOTL? Obviously the United States would need to occupy some territory off the mainland before the American Civil War and Cuba immediately comes to mind, however, wouldn't the US just continue to fight the CSA even after President David flees to Havana due to Cuba's proximity to the mainland? Or could a war-weary populous hold back an invasion in the Caribbean and sue for peace? Another idea that comes to mind is an American colony in Africa, however, how would the African colonies would fall into Confederate hands in the first place?
Anyway, regardless of the plausibility of such a scenario having a Confederate government in exile become a slavocratic pariah state does sound like an interesting setting for a novel IMHO.