I think I would do a trellis with climbing vines in front of the clothes line so that it blocks it from view. Just make sure to put it far enough away from the clothesline so that you have a large enough walk way to bring clothes back and forth. Maybe you could do something that is both pretty and edible, that way it "shoots two birds with one stone" so to speak. Just don't plant anything that birds might eat, like say blackberries, because they could drop the berries on your clothes and poop blackberry poops on your clothes, which would probably stain them.
That's what I'm going to do with my chain link duck kennel. I'm going to plant loads of climbing vines on the chain link (or perhaps on trellis in front of the chain link, so as to keep the chain link clean). Plants that I want to plant anyways, so it saves space since I need to shade the duck kennel from the sun a little. I plan on doing blackberries, muscadine grapes, chayote, malabar spinach, climbing roses, Jubilee fruiting roses, nasturtiums and possibly others that are non-toxic to ducks and edible to humans.
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