The bow from Lothlorien probably was mallorn. As to Mirkwood... the forest itself is supposedly a forest of "beech and oak" therefore, I'd be willing to say you would do well with either of those trees. Yew was a common wood though and, from my own wooden bow, maple is bendable enough to work.
That probably didn't help you very much, but they are some possible answers. I would cast my lot with beech or oak though. And more so with beech because oak is quite the tough wood.
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"And if you listen very hard/ The tune will come to you at last/ When all are one and one is all/ To be a rock and not to roll." --Led Zeppelin "Stairway to Heaven"
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