How to calculate the stability derivative of Pitch Moment with respect to AOA rate?
$q = 0$ means no change of pitch angle. You also have a constant rate change in AoA ($\dot{\alpha} = const$). 

The difference between the pitch angle ($\theta$) and AoA ($\alpha$) is the flight path angle ($\gamma$).

$\theta = \alpha + \gamma$

From this it follows that the flight path angle changes opposite to the change of change of AoA.

$\dot{\gamma}=-\dot{\alpha}$

This is not a manoeuvre that will happen in real life. An approximation of such a situation can happen when after a brief but strong pull-up the pitch angle is kept constant while the path angle of the aircraft is still increasing. The rate of change of the AoA will not be constant in such a manoeuvre.