First, I think you should go to the ICAO website and do some research, yourself. I haven't been there in a long time and don't remember exactly what it has on its site. As I remember, though, it's not very much about SMS considering its importance.
However, as I know, the only requirement for SMS training is within each company that owns an SMS. That means, training should be an integrated part of the SMS, itself. You need initial training for everyone and then recurrent training (I think) yearly.
The training can be anything you want. But whatever it is, it must pass muster by your local regulatory authority (i.e., FAA, DGCA, EASA, etc.). It also has to pass muster by outside auditors who may come to check. So the training must be good enough and done often enough to at least meet local regulatory authority requirements.
No training or certification is required for trainers. But, again, they should be good at what they do so they promote the SMS. As one auditor story goes, the best way to determine how healthy a company's SMS is, is to walk around the company and casually ask non-descript people (for example, hangar cleaners, accounting staff, security guards, etc.) if they know about the company's SMS and what they think of it. The quality of responses from various people in the company will at least show how effective the SMS training is.
