I agree with other posters who say that everyone makes syntax errors, and that relying on documentation is fine (consulting documentation, and not just banging out something that seems to work, is a mark of a good developer)
With that said:
Coding fluency is something that can be improved with practice. Google Code Jam has all the previous rounds available, and there are other similar sites. Do a round once a week, and hold yourself to the time limit. It will be unpleasant, and you might not think you do well, but no one will be watching. That context trains you to write correct code quickly, and you will improve with practice. You'll find that the coding fluency you gain helps your programming more generally.
With that said:
Coding fluency is something that can be improved with practice. Google Code Jam has all the previous rounds available, and there are other similar sites. Do a round once a week, and hold yourself to the time limit. It will be unpleasant, and you might not think you do well, but no one will be watching. That context trains you to write correct code quickly, and you will improve with practice. You'll find that the coding fluency you gain helps your programming more generally.