Sorry if this is old info, but though I've seen mention of red and purple tameable shale spiders, I didn't see anyone mentioning orange ones. The Deep Spiders (lvl 83) in the caverns of Crumbling Depths (northern Deepholm) come in multiple colours. I tamed this orange guy not far inside the entrance:

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I only saw the orange one at the entrance area though. Even though they all share the same mob name, I think they're colour-coordinated to particular parts of the caverns. The rest seemed to be mostly (or all) purple or red, except...
I detected a rare spawn called Jadefang (lvl 85), who is the only green I've seen (apart from the critter versions that are running everywhere). For a long time I couldn't reach him, though I could see his blip. He's very tricky to reach, and it requires both later quest access AND a bit of ingenuity. So don't go looking for him until you're at least up to the daily quest stage of Therazane rep.
Here he is:

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He is tameable, but he's 85, so I couldn't

. Instead I had to settle for killing him, because he also drops a minipet green shale spider:

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Rare, unique colour AND drops a minipet. This guy is gonna be hard to get when Cata goes live, unless they add some more green ones :/