Card Room Green is a muted, sophisticated green with a definite grey undertone, which is exactly what makes it so easy to live with — and exactly what you have to respect when you pair it.
Start with the woodwork. You want a warm but not yellow off-white, and the obvious calls are Farrow & Ball Pointing or James White. Whatever you do, don't reach for All White or any crisp blue-toned white — it'll make Card Room Green look dingy and tired rather than mellow. If you want something even softer and creamier alongside it, Paper III from Paint & Paper Library (LRV 75.3) or F&B Au Lait (LRV 80) both sit beautifully as a light foil on ceilings or adjacent walls.
For a drenched scheme — walls and panelling all in Card Room Green — it's a stunner. The colour has enough depth to carry a whole room without feeling oppressive, and it makes a cracking backdrop for old brass hardware, antique mirrors and aged timber.
Now the accents. Go deep, not complementary. A rich ink or charcoal is the move here — Mylands Cigar BH.20 (LRV 11.8) is a lovely deep, almost-black tone that grounds the green without fighting it. Bring it in on a fireplace, joinery or a piece of furniture. The temptation with green is to reach for a complementary pink, but that's where Card Room Green trips people up — pinks pull out its grey cast and the whole thing goes a bit flat and cold.
That said, if you want a single bold punch of warmth in a soft-furnishing or a door, Dulux Fuchsia Falls 2 (LRV 29.8) can work as a considered, deliberate accent — but use it sparingly and against the deeper tones, not as a wall colour next to the green.
My advice: build the scheme around warm whites, soft stone and brass, and save your one dark accent for the detail. Sample large boards in both daylight and lamplight before you commit — Card Room Green shifts noticeably in artificial light.