A bit of googling gets me this page...

http://www.aidscompetence.org/content/2.13_river_diagram.htm

...where it appears that a river diagram is an Excel Stacked Area Chart
type, where the first area is the minimum across all series, and the
second area is the range between minimum and maximum across all series.
Which makes the stacked sum, the maximum. Then a single series is
plotted as a Line Chart type, showing how close it comes to the "banks"
of the river.

You might want to try a parallel coordinates graph instead of, or in
combination with, the river graphic. Here is a good example from Jon
Peltier:

http://peltiertech.com/Excel/Charts/NewStuff.html#ParallelCoord

This gives you the same info, but a bit more richness. It's like it's
showing you the currents in the river as well as just its banks.