depends on whether you want it game quality or movie quality. Game quality would probably be to create the indentation into the ground plane for the depth of the river, then put a plane that represents the top of the river water and is cutting into the ground plane (banks). Then you could make a river texture and animate the texture.

Not sure about movie quality, might have to use another program for the water animation. I've not really messed around with Maya fluid too much so hopefully someone more experienced in this area can help you out. And I'm not sure that an emitter would look right for a river but you could play around with it. As long as your river bed was sloped downward, and you had gravity applied, the emitter should follow the path.