No you can't. The Notional Organisation of Women would lobby against it. They succeeded in making "manspreading" a misdemeanour and punishable offence for men (but not women) in many US capitals.
So I'm sure they'd have enough clout to stop men-only carriages (or men-only anything) from being commissioned.
The western world is full of double standards, and every complex problem has a simple solution.......that only works