Coo and coup couldn’t really be more different in meaning. The sentences produced when they are used mistakenly can be distracting if you enjoy the surreal.

Coo

• the soft throaty sound made by birds such as doves and pigeons
• to speak in a soft, gentle way; a loving murmur
• (old-fashioned British slang) an exclamation of surprise or amazement

Coup

• (coup d’état) a sudden, violent and illegal overthrow of a government
• a difficult or brilliant action successfully achieved

I am tickled by the idea of pigeons leading a violent regime change or armies taking part in a gentle murmur. But you probably don’t want that in your dissertation or novel. Unless you do …