Going across the color wheel is always a first strategy for color. Across for green is red, but you don't have to use Christmas red. You can use a dark red, or a pinkish color.
Or, you can use blue. Blue and green are great together. If your sofa's color is a green toward the yellow, which olive green is even if it is grayed, choose an aqua or teal. I love aqua with dark green. In fact it is one of my fave color schemes.
https://holhy.com/olive-green-couch/...o-paint-walls/
You might buy some pillows of various colors, take them home and strew them across your couch. See which ones you like. Then take them all back, except for the one(s) you like, and I think you might have a good clue to a color scheme.
Good luck!