The best resource for you is this article on the history of coma identification and treatment throughout history (https://academic.oup.com/brain/article/131/3/877/317052). The word coma itself dates back to 1672 so it was well in use by the 1800s. Other terms that may have been applied to a deep, rouseless unconscious state include stupor and carus. The clinical signs of a coma, like lack of muscle tone, impaired reflexes, and slowed heartbeat, were well known and written about. Different types could be identified depending on the level of responsiveness the patient exhibited. The worst point was said to be when the pupil ceased to contract with light.

One social phenomenon that was observed throughout the 18th and 19th centuries was the deep cultural fear of being buried alive. For the lay person, this would have defined their knowledge of the coma- it was mainly a vehicle by which one might seem dead and then wake up in a coffin. (https://worldneurologyonline.com/article/apparent-death-and-coma-in-the-18th-century/) On the whole, however, this was unlikely.

Coma treatment might include strong smells, pinching or shaking, or in the case of a head injury, attempted surgery to relieve brain pressure. The surgery of choice in the late 19th century was trepanation. Depending on the area and the doctor, bloodletting could still be recommended. It was also entirely possible to just let the patient sleep and hope the recovered. Most of the time, however, a comatose state was a precursor to death, as seen in this case study from 1864, (https://books.google.com/books?id=kjVFAAAAcAAJ&pg=PA146&lpg=PA146&dq=coma+patients+history+19th&source=bl&ots=qAAA-mX6DG&sig=gOBZ4d2biRo1z117fZIaB6yaQLY&hl=en&sa=X&ved=2ahUKEwilqdyE3e3fAhVJx1kKHZToBCg4FBDoATACegQIBxAB#v=onepage&q=coma%20patients%20history%2019th&f=false). Sadly comas are hard to treat, even now, and often accompanied fevers or severe injuries.