I've personally found Depot made great coats to be very, very rare in the Confederate Army. There were some made, for example the Houston Depot made a very small number of them out of "imitation beaver cloth" and the head of the Depot described them as mere ordinary overcoats. I personally am not aware of Columbus or Mobile making any.
The Confederate Army had three principle sources for great coats:
1. Union camps, supplies, and pre-war stocks
2. Imported from Britain
3. Sent from home
Early in the war several States contracted for great coats, most notably in my mind Alabama, but that was short lived. The most common two variants, were several different styles made in Britain on contract, and the Union. For Union acquired ones, sky-blue kersey ones, whether the mounted double-breasted wrist length cape ones for cavalry, or the single-breasted elbow length cape infantry ones would be seen, (And with Federal buttons on them!!!! Sky-blue Federal ones with Southern buttons as "captured" is a dead wrong reenactorism!), with there being some accounts in 1864 of the Confederate Army, most notably in Georgia attempting to dye them "butternut" to avoid friendly fire, and violating the rules of war was common.
As for British ones, I recommend a reading of Fred Adolphus's exemplary research on the subject:
http://adolphusconfederateuniforms.com/the-imported-british-overcoat-for-the-confederate-army.html
Good luck on your search, I know I recently made a replica of the great coat worn by a Georgia cadet late in the War, (Sherman's March) for a friend. I've never had a great coat myself, but I reckon the best one to fit in an impression would be a Union one for Union and Confederate use, and a citizen one as well if you want one that isn't a Yank one or just want to be different but correct. Next time I order cloth I hope to make myself one.