I am not sure what era you are looking for but the only two Marine Corps pieces of equipment I know for a fact fit on regular DOD flatcars (the kind with four-wheel trucks) are LAV-25 tanks (I was an LAV platoon commander at one point) and any version of the AH-1 (Cobra, SuperCobra, Viper, etc). I'm sure there are other options for you, but these are the only vehicles I have personally seen on a regular flat.
The Cobra I saw on a flat was no longer DOD property. It was an older Army version, now part of a fire service. The stub wings were removed. A USMC Viper (the current version of the AH-1) is a lil' bigger than a Cobra, but can certainly look comfortable on a flat. It's well under 50ft long.
To @The Shadow's point, Army and Marine units typically use rail to move armor and artillery units to repair/refit facilities and to training/testing ranges. Unfortunately, helicopters are typically airlifted. That said, YOUR RAILROAD, YOUR RULES, right?
Your biggest concern is really the width of the skids or wheels. Seahawks/Jayhawks/Blackhawks are longer than a Cobra, but are still only about 50ish feet. The wheelbase is close to 10ft though. How wide is a flatcar? The Bell 209 (Army and Navy) is far smaller than a Cobra. Most other helicopters are either too long, too wide, or both. All these are easy to find in 1:48 scale.
Definitely consider using a model kit rather than a pre-built model. That way you can "make it work."
One last thing: you don't have to pick a branch. The Army takes care of everyone.