Paper money is your best bet. Inflation was rampant in the CSA, so coins were pretty scarce as they were considered "hard money" and hoarded. The hoarding was a problem even in the Union, so much so that we went to fractional paper money.
The exception to all of this was California. Since fiat paper money was illegal there at that time, gold and silver coin remained the order of the day. If you traveled there from the East, your paper money was exchanged at a very deep discount.
Essentially the nation had three monetary systems during the civil war, Union greenback fiat dollars, CSA fiat dollars and California gold dollars.