The Confederacy's appetite was always greater than its reach.
The East India Company was out of business (governance of India that is) by the late 1850s following the Great Mutiny.
I don't think a Confederate version can develop in the 19th century since the EIC was a unique, the only other similar company would be the Hudson Bay Company. These companies had virtual monopolies in their respective fields and were practically without any major rivals (keeping the history of the HBC simplified). Free trade was the death knell of such monopolies as the EIC and the HBC. Exactly what would some Confederate East India Company trade anyway? Also, under the Confederate Constitution, I don't quite see any such monopoly ever being permitted to exist unchallenged.
Throughout its history the EIC was closely associated with Britain, so there is no possibility of some renegade Confederate corporation (probably based on the Kramer Corporation of For the Want of a Nail) developing without ties to the Confederate Government. The development of such a company would be detrimental to the Confederacy.