Over the years more than half of the Southern's passenger cars were supplied by Pullman-Standard. The Heavyweight Cars were Pullman Green and as the poster above said they appeared almost black[kind of a faded black in my memory] and had yellow gold lettering. You can verify this in the book "Southern Railway Color Guide to Freight and Passenger Equipment" by James Kincaid, it has numerous examples in color.
Heavyweight Cars were also built by St.. Louis Car Company, Bethlehem Steel and others such as American Car and Foundry who built Lightweights postwar also.
The only Southern Railway model passenger cars that I have found over the years in a Pullman "Green'' is a 5 car set by MTH. Of course, there are many sets in the Lionel, MTH, K-Line, etc, versions of the green Crescent Limited as well as the stainless Lightweights in natural, some with black painted roofs.
The first Southern stainlless Lightweights were delivered along with the E6s for The Southerner[Mar '41], The Tennessean[May '41] and the Crescent, no longer called the Limited[Dec '41]. Pearl Harbor and WWII put a stop to all car deliveries[and most engines] which actually did not resume on cars for the Southern until 1948--postwar there was a real car shortage.
In a few cases such as on The Tennessean, Heavyweight Sleepers were painted in silver to run in the Lightweight consist of the name trains---the "Silver Trains". Heavyweights ran mixed in stainless consists well into the 1960s and beyond. SRR President Brosnan even had container car freight in tow behind passenger consists. The profitable revenue was in the headend cars [mail and express] not back in the coaches. As result photos show 4-6 Heavy weight RPOs, REAs, Combines and Crew Cars in Lightweight passenger consists. Airmail and trucks gradually ended that scene.
Keep in mind that the Crescent Limited adorment on the Ps-4s and Cars we model was to mostly disappear by 1934 as the Great Depression really cranked up. Anyway there were only four "Harrison" Crescent Limited Engines decorated, two out of Pegram Shops Atlanta and two out of Spencer Shops in N.C. Three "Harrison" Southern Ps-4s carried the "Queen and Crescent Limited" decoration over on the CNO&TP and the AGS, rostered in the Ferguson and Finley Shops.