I've towed my 2-man kayak (actually kind of a hybrid between a canoe and kayak) behind my bikes using a two-wheel canoe cart. The cart is basically just a frame with the wheels on the sides and the boat sits on top of the frame. I attach the bow of the boat directly to the rails of my bike saddle with some rope. That provides enough flexibility to be able to turn corners, but is tied tight enough so there's no excess sway. It tracks very nicely and I've never had any control issues.

A regular canoe has a deeper bow than my boat so you'd run into clearance issues over the rear wheel of the bike. But I'd think you could securely strap a bar that extends from the bow of the canoe and then attach that to the seat rails.