what is the fastest way to cool down the coffee in a cup with just a spoon ?

Yes.
Stir it. The metal of the spoon attracts the heat.

When my dad was an engineer at OMC Research (Evinrude outboard motors, Lawnboy lawnmowers, etc.) before they were bought out, they bought a program from Yamaha about heat transfer. And one of the things they did when playing around with the program was figure out the heat transfer of a spoon in a cup of coffee.

In Physics you learn that stirring a liquid fast enough can actually heat it up because it gets the molecules moving. Although, just stirring hot coffee in a cup would not really be enough to notice that, but it would improve heat transfer to the spoon and cup where heat can be radiated off.

Just stir it .. and it helps if the spoon is a cold metal one.

Stirring will keep bringing hot to the surface, where it would cool, and take the cooler molecules inside.

Hmm I don't know about that...I usually put a few ice cubes in to cool it down though.