Copperheads over osage can make one of the prettiest limbs combos availible. If your worried about the brightness of it there are processes that can be used to speed up the darkening of osage. In all honesty though, my limbs are bamboo backed which are actually brighter than osage and I've not had problems getting within range of and drawing the bow on deer, pigs, squirrels, rabbits, dove, crow, or a few pest animals over the years.
If you want something a little darker that works well with osage, pick any of the reddish woods and you could do an osage riser with accent stripe or flair and limbs to match the accent. Cocobolo, ebony, ironwood, bubinga, cedar, tulipwood, etc all look really nice with osage and could darken the limbs a touch if that is a concern for you. You could even do the accent wood on the back of the bow facing the animals while leaving osage on the belly for you to see so you could have a darker bow to blend in while still being able to see your choice wood.
I have some really old osage that has darkened so much that it looks like dark black walnut where it was exposed to light/air in my knife shop. When you cut it though the inside is bright yellow. You may could just have the bowyer darken it before putting on the finish as well.