You might try describing the tail as a bone that helps balance the body. "Graag qeth do kopraan-ro" (green bone of body-balance) is one way that might work. Of course it's the fur or skin that would be green here, so you could try "graag slen do kopraan ro" (green flesh of body balance)

EDIT: I'm slowly warming up to "laatsekopraan" (last of the body) for a shorter way for tail, but if you use it you'll still need to provide context that it's a tail and not, say, the foot or butt.

To be specific it's to be used as name - my overall nickname is GreenTail, so it's quite the pain that there's no 'tail' in dragon speech..

'graag slen do kopraan ro' sounds good as translation, but it's kind of long for name, and i'd rather place it 'alone' (GreenTail and no word more), so providing context is not much an option.

Nevertheless thank You for yarr ideas. :)