You can buy a water drill for pretty cheap. You hook it onto a drill moter and use a garden hose. I have done it a few times, its not fun. But it does work.
You need a trench on the side you are feeding the conduit from and a big hole where you are trying to "catch" it. So if its a small area you are probably out of luck.
Also, you don't have a lot of control exactly where you end up. Though my dad likes to tell the story of the time he did it under a schools parking lot that was 150'. He was only a few feet off.
Unless you feel really lucky or the driveway is an expensive material, I would lean towards cutting the pavement. Its hard work, messy and not fun having an electric drill down in a water soaked trench.
