I built a co-axial rotor gyro back in the 80's and it just BARELY flew. If I could get it up and flying in a straight line it would hang in there until I tried to turn it; then it would continue to roll slowly after releasing the rudder input. As I added more & more opposite rudder, it would get into a crossed up slip and finally crash in a knife-edge attitude. I built mine with a larger upper rotor dia. to compensate for the loss of effectiveness due to rotor wash from the lower blades. This is supposed to work, theoretically, but I guess all that was negated by my use of Gorham "Cricket" helicopter rotor blades (heavy!) I've since been told they don't even work on the helicopter they were designed for.

If I were you, I'd take the easy, proven method and use Randy Wrisley's "Gyro Schtick" rotor. Easy-peasey and it flies GREAT!. Just a disc of .032" fiberglass with 3 flat bottomed blades and shims under the trailing edge