I like, many people have gone through my entire live hearing people call coffee "Joe" without ever asking why. My initial thought would have been that it was a variant of "the average Joe", maintaining that the average person drinks coffee. The answer goes a bit deeper than that.
The image above is used quite frequently with coffee-related posts around the internet, and for a good reason. Coffee wasn't a big deal until the WWI, when soldiers were allotted less and less liquor by the US government. In 1914, Secretary of Navy Josephus Daniels banned alcohol completely and soldiers were left with coffee to pacify the craving. One story suggests that soldiers began to refer to coffee as "Joe" as a form of mockery.
Whether or not this story is completely true, it is no secret that the military has had a huge impact on coffee culture in the US. Next time you call it a "cuppa Joe", remember the people who did first.