I've heard decorators say green is a neutral so anything goes with it.
Hi Linda. I would go with a tan or neutral color.
Depending on the room's use, your likes (and dislikes) and your budget, you can use the color of the furniture as an accent and decorate with neutral colors while picking up the love seat color hear and there - or you can create a patchwork with two or three colors and scatter them around in a thematic way. If the greenish is really bold, the better choice would be to use them as focal points. If it is more pastel, then a tri-color pallet might be better. The theme idea works either way. Homey, modern, classical, eclectic, beach, farmhouse - you get the idea. Your house - make it comfortable for you!
Pull out an old fashioned color wheel! Choose complimentary colors.
Use florals, the greens would go beautifully. You can get contemporary as well as traditional. Just do one wall or just curtains. Pick out another colour in the fabric or wallpaper and use to bring the colours together on cushions and ornaments, rugs etc.
Tans/beiges, complementary shades of grren, blue, yellow should work. Grab a large number of paint chips in colors you wish to try. Tape them to walls and check throughout day, evening, both with and without interior lights.
Soft whites are another option (see Sherwin Williams or Ball and Farrow paint sites).
Small shots of black are sometimes useful, depending upon thevlook you're seeking.
As Sal suggested, any colors mimicing an outdoors setting should work, so long as colors don't clash.