A single Irish chain in just green and white would be beautiful. If the green were the main color that would be backward but very interesting. I would rather break the rules and that sounds beautiful to me. drunkards path would be great too but the curves might be a little much if you are really new to quilting.
A nine patch is kinda like an Irish chain but if you put sashing between maybe a green hand dye in almost the same green, that would give it a little variety.
But you know if it's not what he asked for ...
My son keeps telling me he doesn't want a quilt. If he asked me for an all one color 9 patch, I would probably make it.