Paint an accent wall behind the dark green couch a soft brown or beige color. The neutral tone frames the couch without competing for attention.
Add accessories that contain touches of red around the dark green couch. Hang an abstract painting with dark red accents on the wall behind the couch. Or place a vase with red roses or carnations next to the sofa. A few accents of red will add dimension to the color scheme.
Soften the dark green by draping a cream-colored afghan or throw blanket over one end of the couch. Throw pillows in the same shade provide an airy counterpoint to the more grounded dark green color.
Place light-colored wood end tables and a coffee table, such as oak, around the dark green sofa. Dark wood tables beside the dark green would have a somber effect but light-colored wood tables will provide a pleasing contrast to the green shade.
Set an oriental rug in front of the dark green couch. The multicolored floor covering with a hint of the same shade of green will offer a pattern to break up the solid color of the couch.
Hang antiqued dark gold lantern sconces behind the couch. Place colorful hand-painted ceramic lamps on one or either side of the sofa or opt for neutral-colored lamps with dark red and beaded or fringed lampshades to add a frivolous tone to contrast with the starkness of the dark green sofa.