C172's are tough to spin, especially to the right.
I usually set spins up like a power on stall (in cessnas and other aircraft that are difficult to spin). Once the stall is full developed, I kick in full left rudder making sure I continue to hold strong back pressure on the yoke while doing so. Going to the left allows you to use P-Factor, Spiraling Slipstream, and Torque to your advantage in entering the spin.
Once the plane is inverted, I reduce the power to idle and continue to hold full left rudder, full back pressure on the yoke, and left aileron input. These control inputs should keep you in the spin. Recover after 2 or 3 rotations by bringing the ailerons to neutral, applying rudder oppiste the direction of rotation, and pushing briskly forward on the yoke to break the stall.
You need to be sure to hold back pressure on the yoke the entire time or you'll just go into a high-airspeed, nose down, steep spiral.