You could try that sticky fly paper but it gets to looking pretty ugly once some flies become attached. the best solution, of course, is a screen door. What does a baggie of water do? Very curious because I don't have a screen door for my sliding glass door to the backyard and flies are a huge problem in the summer. I have used those bag-type things you buy at the hardward store where you fill it with some sort of solution and hang it up. It attracts the flies and once they fly into the bag, they can't get out. I don't know if it's "green" though but it does work great.