Its all speculation...
Confederacy forms alliance with the United Kingdom
Mexico attacks the Confederacy in an attempt to win back territory in the South Western United states.
Mexicans are driven backward and defeated.
US and Confederacy clash in the 1880's in a Second War. Conflict ends in stalemate. The War is fought over Expansion rights in the Western Half of North America.
Politics in the Confederacy is dominated by two groups: The Industrialists, who feel that the Confederates should focus on growing an industrial base to rival the North and the agriculturists, who still view the South as an agrarian society. The Industrialists will eventually succeed and as a result of necessity the Confederacy will become more industrialized than it did in Plane-zero USA.
The North (or the US) will continue to grow industrially fueled of course by the influx of European immigrants in the 19th century.
US and Confederacy agree to divide the Western states amongst each other. The Northwestern States and California will fall under US Domination. The southwestern and several mid-western states will join the Confederacy.
Slavery will eventually be abolished in the Confederacy but only in the 1920s after several devastating slave rebellions bring chaos to the Southern States. International pressure and a changing political scene will force the Confederacy to drop its pro-slavery stance.
Texas will break away from the Confederacy in the 1910s and form a new nation the Republic of Texas.
Without a dominant power in North America, the European countries will become more involved in South America. Major players will include Britain, France and Germany.
The Confederacy will enter the First World War at an earlier stage than the US did in reality.
The reason for this early entry by the Confederacy is motivated by a need to assist the British Empire, the South's most significant trading partner.