So they question is - along with how a CSA even survives as an independent nation, which no one ever can provide convincingly - what in the world is such a "nation" going to live off economically in the Nineteenth Century?
God how often does one have to answer this silly question?
So assuming a European intervention, Californian freedom and a large Confederacy as described in my post above.
Cotton
Cotton brokerage (as the USA will be an independent nation it will be unprofitable for the Southern merchants to sell it via the exchange in NYC)
Trans-Atlantic shipping (as they won't want or need to trans-ship through NYC anymore)
Cotton textile trades (an ideal use of slave labour)
Coastal shipping and probably across the Gulf of Mexico
Fisheries (the coast of the CSA will be 3 to 4 times longer than that of the USA)
Riverine shipping including fees for transhipments of USA goods to the sea via the Mississippi
Molasses
Refined sugar
Tobacco
Finished cigarettes and cigars
Ground nuts
Beef (sell north to the USA as in OTL and south to the British Colonies both export trades) and internally this would be a very cheap way to feed slaves
Hogs
Iron ore mining
Coal mining
Iron and steel production and processing
Some hardwood logging
Sulphur mining (pre-Frasch process)
Sulphuric acid production
Copper mining
Copper processing
Hemp cultivation, textile and rope production
Paraffin production
Wolfram (Tungsten mining)
Lead mining
Zinc extraction
Silver mining
Bauxite mining and aliminium processing
Petroleum processing
Railways
Hydro-power
Ship building (coastal to start with then oceanic)
Armaments
Possibly importing other agricultural crops suitable for slave cultivation - tea, coffee, cocoa and rubber are the obvious ones
Holidays in the sun waited on by slaves for rich northerners
&c
The USA on the other hand has serious problems, massive war debts and possibly an indemnity to pay off. Only one major export earner - grain. Loss of two of the main streams of government funding import tariffs (because the USA's merchants have little money to buy imports) and Californian gold. The third stream government bonds is going to be seriously reduced too as the will have trouble paying off war bonds.
The CSA has debt problems too but has the wherewithall to get out of them.