I can't help too much because I avoid 'tragic' characters for the same reason that you do, but don't get hung up on being 'cliché'. All that means is that you're doing something that's been done before, really, and, yes, tragic characters with bereavement, drug issues, rape, genocide, [i]whatever[/i], have been written before in fiction. No matter what character you right, somebody out there will be able to say "Oh, like character x from artistic work y."

What you really want to do, in my opinion, is to write whatever it is well, whatever the particularly tragedy is. Poor writing, not content, is the aspect of Mary Sues with tragic backstories that elicit my groans. It's not the fact that she walked out of a genocide that makes me go "Ugh, really?": It's a pretty horrific thing to happen to somebody (even Sue) and easy to sympathise with, unless the author jeopardises the reader's sympathy and understanding of the situation. I know 'write it well' isn't the easiest advice to act upon, but it's the best I can do. :P