I'm not on the River Police, but ...

It'd be possible across one particular geological era if you were to get your bedrock elevations right. It's all just a matter of gravity. Rivers flow downhill. Just make sure the elevation of the terrain runs from high to low along the length of each river, and make sure the elevations are equal where the city is. Simple!

Eventually, erosion would alter the system, given enough time and lack of interference by terrain engineers.