This depends on the accuracy and sounding density requirements, the width, depth and current velocity of the water body. I have done a fair bit of river hydro-work with both single beam systems and sounding rods / chains. This sounds like a sounding chain problem. I would be more than willing to help with some more details about the river.
We've done a few base maps for bottoms of lakes and reservoirs using an EDM, shooting to a man in a float tube, holding a prism and a cloth tape with a weight on the end. The EDM and prism give the location, the tape and weight give the depth, which we subtract from the lake elevation to get bottom elevation. You could try this on your river if your site is small, but the water surface elevation may not be constant if your river site is large or has significant gradient. Also, bottom elevations of rivers are likely to change with river flows.
Are you trying to get a cross-section of the river or a profile of a centre-line of a stretch of river? Hummingbird sells portable fishfinders for under $200 that are suitable for this use. With one of these units all you need is method of horizontal and vertical control that can be supplied by conventional survey methods. What is the width and velocity of the river? Do you have any guess as to depth?
