The easiest solution is to build your city where existing geography supports your goals. The most obvious (and extreme) example of an overflow-proof river on Earth would be the Grand Canyon in the Southwestern United States. With the walls of the canyon rising an average of 670 meters above the river bed, there’s no chance of it overflowing a hypothetical city built above it.

You’d want something similar, though probably not as extreme - a river cutting through (and eroding) hard rocks to create high, nearly vertical canyon walls that prevent overflow. The specific rocks and age of the river would determine how high the canyon walls are, so adjust as desired. It took the Grand Canyon anywhere between 6 and 70 million years (depending on who you ask) to develop into its current state, so adjust your time scale as necessary and you’ll get what you want.