You say the only lumber you can get is green lumber.
Do you mean green treated lumber, or do you mean poorly kiln-dried lumber?
Green treated lumber is becoming less popular, and to be honest it is crap to build with unless you get "last years" stock and can cull out the 75% that is twisted and warped. Treated lumber fresh from the mill has so much water and chemicals in it that if you hit it with a hammer, very often it will splash moisture into your face. That is not a good thing, since that is probably arsnic splashing into your eyes.
The lumber is so bloated it is forced to be straight. As it dries it looses nearly half it's weight, and it twists, bows, splits, and checks. I have screwed down deck boards one day, and come back the next to find deck screws broken from the board twisting overnight. Sealing it will only slow down the process, not stop it.
I have pretty much gotten away from using treated lumber period, with the exception of posts that go into the ground.
If you are using untreated lumber that has been poorly kiln-dried, find another source. White pine or Poplar has been used for a century to build houses. It will hold up as well as treated wood as long as you paint it and maintain it. Cedar is excellant, although it is more expensive and does not have quite the strength and rigidity of Poplar.