The Louisiana State Archives in Baton Rouge has in the reference room a set of books on ships that were registered in the Port of New Orleans between 1820 and 1900. If you check that set (I do not recall the exact name of the 5-6 softbound books), they have listed very detailed information about ships and their owners that passed through New Orleans at some point. It won't help if those ships did not pass through New Orleans, but if they did, it is a treasure trove of information.
In W. Craig Gaines' landmark book "Encyclopedia of Civl War Shipwrecks" (2008, LSU Press) it lists the CSS Darby (p.62),
"CSS Darby. Confederate. Steamer. Armed with three guns, including a 32 pounder brass gun. Used to transport stores, ordnance and troops. Was burned on April 17, 1863, on Bayou Teche near Bayou Fusilier above Breaux Bridge to prevent its capture. (Ofiicial Records of the War of the Rebellion, Vol. 15, Page 343/Civil War Chronology, 1861-1865, Vol. 6, Page 218).