Instead of going to the length of explaining the physics and using some kind of unobtanium device, you could have a micro black hole (say the mass of a small planetoid) as the threat, and then deflect it by propelling a series of big objects (say, most of the asteroid belt for starters) close past it , or leaving a really big ship near it for a couple of years. Gravitational attraction does the rest!Secret world leader (shhh) said:The idea is that the Black Hole is created by a thing that implodes and becomes a black hole, the device to stop it is one of those, but reversed. They are of equal power and should cancel eachother out. It doesn't entirely matter if they do or don't, the device never actually explodes, i'm just trying to have a reasonably plausible setup.
Obviously you need rather impressive engineering, a lot of time, and the black hole to be moving pretty slow relative to the Solar System to do this, but on the bright side it's a relatively hard sci-fi strategy that could conceivably be used to deflect asteroids [http://en.wikipedia.org/wiki/Asteroid_impact_avoidance#Asteroid_gravitational_tractor] today with enough warning, so you're using founded principles.
ON an unrelated note, 'The Black Cloud' by Fred Hoyle is a good old-school sci-fi story about an imminent calamitous event (big cosmic gas cloud instead of a black hole) - grab an e-copy if you get stuck and need some inspiration!