Is there a simple relationship between angle of attack and lift coefficient?
In the post-stall regime, airflow around the wing can be modelled as an elastic collision with the wing's lower surface, like a tennis ball striking a flat plate at an angle. Lift and drag are thus:

$$c_L = sin(2\alpha)$$
$$c_D = 1-cos(2\alpha)$$

I superimposed those (blue line) with measured data for a symmetric NACA-0015 airfoil and it matches fairly well. I don't know how well it works for cambered airfoils.