Here's how it goes in my TL (this is from memory, so some details might be wrong):
The South wins using the Turtledove POD. The peace treaty is signed in 1863 in Brussels. The North is left to occupy west Virginia and east Tennessee for 20 years, when plebiscites would be held to establish the fate of Virginia, Tennessee, Kentucky, Missouri, Indian Territory, Greer County (disputed between Texas and Indian Territory), and New Mexico (the Confederate one). The 4 states have twin governments during those 2 decades. When the plebiscites are held, Kentucky and Missouri remain in the Union, everything else goes to the Confederacy. The US had not abolished slavery or given blacks any rights during those 20 years so as not to alienate the locals (all bets are off after the plebiscites are held).
The Confederacy gains Cuba during a war with Spain. Afterwards they decide to invade Haiti and eliminate it as a threat. With help from France and the US, the Haitians kick their asses. Haiti becomes the CSA's Vietnam. Led by a character that I've taken the liberty of introducing, the Haitians unite the whole island (Spain had left Santo Domingo after losing Cuba) and force the Confederacy to evacuate in shame. "Haitian tactics" (a more brutal version of what how the Viet Cong operated) gain worldwide recognition, and the myth that blacks can't fight is destroyed.
A new war in Mexico between the imperialists and the republicans leads to northern Mexico (Tamaulipas, Coahuila, New Leon, Chihuahua, Sonora, and Lower California) seceding and forming the Sierra Madre Republic, which soon negotiates its union with the CSA.
Nicaragua is invaded by the Confederacy in the 1870s. Attempts to take the rest of Central America are failures. The Confederate threat is one of the reasons why the other republics in the area form their own federal state. The CSA also supports Panamanian secessionists in Colombia. The North sends marines in support of the government (based on a pre-POD treaty). The secessionists are defeated.
Further attacks on Haiti and filibustering expeditions in Latin North America are also failures.