I started a Jewel Box with green and unbleached muslin and it looks great.
http://quilting.about.com/od/quiltpa..._box_quilt.htm
There's always Storm at Sea (regular pieced or paper pieced). Traditionally that pattern is done in all blues but I would think the green would look nice.
http://www.quilt.com/Blocks/StormAtS...irections.html
There's an old pattern called Village Green that uses all green prints. The block consists of triangles going around a plain center square. I tried doing a google search but all kind of house quilts came up instead. I don't know what the name got changed to. I have the pattern in an old book at home that I can scan into the computer and post if you're interested in seeing it.