I'm not sure where you are, so these may or may not be close...
Camp Hi on the upper Cuyahoga near Hiram rents canoes and kayaks for trips on that river.
Crooked River Adventures in Kent does the same.
Stark Parks rents canoes and kayaks at Walborn Reservoir near New Baltimore (also at Sippo Lake in Canton)
The Grand River Canoe Livery (I've never used them):
http://grandrivercanoe.com/
You can rent canoes and kayaks at Presque Isle up in Erie, PA.
I'm sure there must be places on Pymatuning Reservoir also, but don't know of any first hand.
Hope this helps.