To do what you want to do you first need to go to Advanced, then you just un-check enforce water heights. Then once you've done that click on the shallow water tool, now make the basic shape of your river or whatever you're making. Then once you've done that, use a tile to line the edge of your river so you know where to lower it later.
Now, use the cliff tool to fill in the river, then use the lower tool to lower the land where your river was. And there you go, you have your river
~Deathcom3s