Hi Rosie!
Unfortunately, I have never met such a case before. After a quick literature review, I found that this recurrent atraumatic subluxation is very rare. The patient's age is indicative of a possible fracture at the epiphyseal plate which is misinterpreted without an x-ray or CT. I guess this has already been performed but if not it is highly recommended. If it is ligamentous laxity, I assume it will not be rehabilitated non-surgically. On the other hand, surgical intervention has many contras for this joint. As for taping, I have never learned or used it for the SC joint.
Therefore, I could only guess of what could help your patient. Stability at the SC joint is accomplished almost exclusively by the joint's ligaments and disc. Taking this into account, motor control training of the shoulder girdle might not have a high impact on SCJ stability. However, this joint participates in arm elevation and a therapist should definitely attempt to increase motor control of the area. PNF patterns and techniques might help you a lot in this. As for taping, I cannot think of a way to 'stabilize' the tape to a firm point. It could be the sternum or the ribs but again I doubt. Mobilization of the joint might help through a Mulligan-concept mobilization with movement during elevation of the arm. Try to palpate the direction of subluxation during active movement and then apply a sustained force against the direction of subluxation and repeat arm elevation. Just try to insist excessive motion, do not apply a high force and ask the patient if it's painful. There's no other way I could think of facilitating this movement. Classical interventions like ultrasound, TENS for pain etc don't think they should work.
I hope I helped in a way. I'll keep on searching.
Regards