A pieced tree would look nice. I had to chuckle to myself when I read DottyMO's idea. Thinking about getting all 2,500 or so names we'd have by listing all our past & present members from the last 10 years onto a 10x30" quilt would be a challenge in itself. But if you have a smaller guild that might work.
As HillCountryGal wrote, there are many options for a green quilt if it doesn't have to be appliqued -- or even if it does. There are many scenes you could create using only variations of green. Think Picasso's Blue or Pink Period, and then just make sure to have plenty of contrast in saturation to add interest; and it might also be good to add visual texture with various sized prints and some solids. It doesn't have be a recognizable object -- just start sewing and see what emerges. You might be surprised!
Oohhh! One more thought -- what if you got a solid wholecloth & did quilting in different shades of green thread?