Coster Shops Knoxville,perhaps the first green engine done there. http://cmdc.knoxlib.org/cdm/singleitem/collection/p265301coll7/id/3616/rec/5
I would say you're right, if it's 1926. The first green passenger engines on the Southern were the Fairfax Harrison Ps-4s built by Richmond Works that same year. Those particular engines are exemplified by number 1401, in the Smithsonian. Harrison decreed that all front line passenger power get the same green paint, so indeed the 1201 might be the first.
Not all Pacifics got painted green, however. The low-drivered engines like the 1298 that worked Appalachia Division trains 1 and 4 retained black paint (but with the fancy stripes and trim).
Looks like the wheels and drivers got some green paint too.
Never knew that.