Don't you mean allow the river to be smaller (i.e. flow faster and have less width and therefore less exposed surface area)?
I wonder what sort of options there are for shading a river? Floating solar panels are used in some places, and have the advantage that it's relatively easy to rotate a whole floating structure to face the sun rather than having to mount every single panel on a heliostat.
More houseboats would be a possibility, but the number required to make any noticeable difference would effectively turn a river into a city, which could have other negative side effects.
Setting up floating barriers and growing azolla or some other water-covering crop might be an interesting option. Not sure how much that would affect temperature, though; it might even cause more heating as the dark leaves convert more light to heat than open water. Also the water might move too fast or be too turbulent to be able to grow water plants. Or if successful, it might cause more water to be lost by evaporation.
(In a lot of cases, removing dams might be the best option, but some dams like Bonneville or Hoover are producing substantial amounts of energy and it would be pretty hard to do without them.)