How many resonating structures of Carbon Monoxide are there? Anywhere I look, I get 3 resonating structures for CO molecule, like in this answer.
However, according to the rules stated for drawing resonating structures in this site, I wonder why there can't be this resonating structure as well?

Although it will be very unstable (due to lesser number of covalent bonds, positive charge on more electronegative atom), yet a minute contribution of this structure must in present in the resonance hybrid of the CO molecule. Then why is this structure not shown anywhere?
You have said it yourself. There are many possible resonance structures but most of them have a negligible contribution to the overall structure. Your proposed structure is one of them.

The major resonance contributors of carbon monoxide are: $$\ce{\!\overset{\ominus}{C}#\overset{\oplus}{O}\! ~&lt;-&gt;~ \!C=O\! ~&lt;-&gt;~\!\overset{\oplus}{C}-\overset{\ominus}{O}\!}$$