As the former river rat, here's one of the versions of the prayer I used when offering libations to the Tallapoosa River.

Arkheloos of the living waters,
ruddy god of the tangled locks,
ever stumbling in your rocky bed,
child of Oceanus and the Oreads,
favored by the rains of Zeus,
you purify us in our rites
that we might approach the gods.
Recieve my offerings with favor
and look with kindness upon here.

According to the book Greek Folk Religon Arkheloos was well on his way of becoming The River God by Fifth Century Athens so I started addressing all rivers by that name.

Tangled locks is suggested by overgrown banks. The Tallapoosa is shallow with frequent shoals and the third line shoul be changed to reflect the river being addressed.  On the Chattahoochee I once used "You hold a share in the works of Hermes" referring to the commerce conducted on the river.

I used the Oreads as the River's mother here because it issues from the caves and mountains of North Georgia.  Tethys would be more traditional.

Chris Marbutt