This was the product of Joseph Burnett, of Boston. Burnett started selling the product in 1856. According to the product label, Cocoaine was entered according to an act of congress in 1857. When the Trademark was registered in 1927, they claimed to have been using the brand name since 1847. I think that is extremely inlikely, since Burnett brought his preparations to an Exposition in 1850 and the Cocoaine was not listed.
A couple of years after the product was introduced it was imitated by Phalon & Son's product: Cocoine. An ad in the 1860-61 Boston City Directory (view) told about how Burnett had won an injunction against the Proprietors of Cocoine for trademark infringement. Apparently, this case was like a landmark case for the law regarding trademark infringement. The Phalons had to change the name of their product.
Burnett's Cocoaine sold for over 45 years and was one of the most successful hair preparations of the 19th century. Burnett's Cocoaine was still listed for sale in the 1901 Morrison & Plummer catalog.