Should the pitching moment be up or down? I had a question regarding the direction of the pitching moment. 

To make sure we are on the same page, here is what I know so far (please correct me if I am wrong).


Lift acts through center of pressure
Normally moment is taken around Aerodynamic Center because then the moment does not vary with angle of attack.
In a cambered airfoil, the aerodynamic center and center of pressure are not at the same place, so the lift created also generates a moment at the aerodynamic center. 
In a symmetric airfoil, the aerodynamic center and the center of pressure are at the same place, so you do not have a pitching moment.
Location of Aerodynamic Center is fixed for an airfoil, it does not change with speed. 


I am trying to understand the concept of longitudinal static stability and in all the diagrams, the pitching moment is shown to be nose up.


But I would imagine that the center of pressure is further downstream on a airfoil than the aerodynamic center, so shouldn't the pitching moment be nose down? As shown in this picture


Thanks for your help,
All points you mention are correct (for the nitpickers: Point 5 is only true below transsonic speeds). That the pitching moment of the wing is drawn nose-up is probably because it is positive this way - nothing more. The sketch you posted in your question is rather poor, with the center of gravity located behind mid-chord when it should be closer to the aerodynamic center.

Indeed, if you have positive camber, the center of pressure of the wing is behind the aerodynamic center, so the wing's pitching moment around the aerodynamic center should be nose-down. However, if you assume the center of gravity of the isolated wing to be at mid-chord, the center of pressure is normally between the quarter chord and mid points, so the wing all by itself will pitch up because it pitches around the center of gravity. The moment depends on the reference point.

Did you look at this answer for an explanation of static stability yet? Let me know if something is left unclear.