The expression is "Cry me a River". If you say any other body of water, it'll be understood but will be assumed to be a joke. I assume you would intend it as a joke, right? However, bear in mind that the world is unfair to foreign speakers of a language. Sometimes you might intend something as a joke but people assume you've just made a mistake. Your listener might not understand you're being funny.

If I were you I would just consider "cry me a river" to be a set expression. Any other way just sounds weird.