Cleaning it once a week isn't a good solution either. It's just prolonging the inevitable--even for a small goldfish, a 10G is no way to live a good life. 20G is bare, bare, bare minimum for one fancy goldfish, and not a good permanent solution because goldfish are social animals and need to interact with their own kind. If it's a comet or a common goldfish, keeping it is -completely- unrealistic and you should focus on rehoming it.
If you can, you should really do some specific research into goldfish care. Try doing some reading around here: http://www.kokosgoldfish.invisionzone.com/forum/
so that you can better understand the needs of the goldfish so you can make a more informed decision about the fish's future.