Fresh hot chicken poop will only kill the plants you don't want to kill. Re: the weed that you want to kill, it's helpful to know about the weed's behavior: How does it reproduce? Seed, underground runners, vegetatively, some by all of those methods, and a few others besides! Is it Annual, perennial, Biennial? this knowledge will help you know how to mount an attack. Also, knowing what growing situations it LIKES is helpful. Give it a lot of what it DOESN'T like! You might try putting some thick layers of cardboard over the weeds, and then covering that with at least 4" of chicken bedding. An other option is to cover the area with old carpet for several years. You can try solarizing it, but under a tree, that might not be successful. Perhaps successive crops of green manure to starve and shade it out.