If you want to get an official headstone for a Confederate veteran, you can get one through the Veteran's Administration. You have to provide the documentation for the veteran. There is no organization whose "job" it is to put markers on these graves. If you want a marker put on a grave, you are the one "responsible" for getting it done. But the VA will help, and will provide the marker free of charge. Contact the Parish VA Officer in the parish where the gravestite is located for more information.