The short answer is that it depends on the mass of the black hole. A stellar mass hole would have no effect because the force would be tiny, as rod points out.
On the other hand, a galactic-core-sized super-massive black hole would be a different story. Gravitational force varies as the square of the distance between the objects. Our sun is 150 million km away. This is roughly 1.6 x 10^-5 ly. To exert the same force on the earth from 2 ly away as the sun does from 0.000016 ly away, the hole would need to have a mass of about 16 billion suns.
This is within the estimated range of super-massive black hole sizes, so if a monster like this suddenly appeared 2 ly away, things might not go well for us.
This new gravity source would pull on all objects in the solar system, including the sun so where it appeared would probably have a significant effect on the outcome. You'd have to punch the numbers into an orbital mechanics simulator, or be a lot better at orbital mechanics than me, to get an answer.
If it appeared such that the earth was directly between the sun and the hole, I suspect that the earth would stop orbiting the sun and merrily head off into space. The further it gets from the sun, the greater the influence from the black hole and I would expect that, after a suitable amount of time, the earth would stabilize in a highly elliptical orbit around the black hole, along with all the other mass in the solar system. It wouldn't matter to us because we would all have frozen to death as we left the sun behind.
Fortunately, black holes don't just appear, they have to have a source of all that mass and there's nothing within many light years of us to supply that much mass.
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