The stiffness value you want depends somewhat on your purpose for finding the stiffness, particularly if the load-deflection relation is nonlinear.
For many purposes, it is useful to define an average stiffness that represents the average slope over some working deflection range, whatever is appropriate to the situation appropriate to your problem. This would be the slope of a chord to the load-deflection curve, rather than the slope at a point. Obviously it will not be exactly correct at more than one point (the mean value point), but it will be somewhat close over the whole range.