There isn't a definitive answer to this. The first recorded use that I'm aware of was in 1931.

There was a theory, which seems to be widely regarded as false nowadays, that US Secretary of the Navy Josephus Daniels, banned alcohol on navy ships in 1914, So sailors began calling coffee by his name.

Another theory is that it is a slang combination or shortening of either or both of the words "java" (slang for coffee since the island of Java grew a lot of coffee beans) and "jamoke" (which is, itself, a combination of the words Java and mocha).

The third theory, and the one I've seen the most support for (although personally l don't understand why this one seems the most likely to people) is that it is just a a play on the phrase "average joe." As in, coffee is a drink for your average American guy ... I guess.

I personally believe it's something like the second option. It was probably just a random slang thing one guy or group of guys came up with that doesn't make a lot of sense, but that other people like and kept using. I remember this happening personally with slang words when I was growing up. Words would be substituted for other words by one group, often without much rhyme or reason, and for some reason or another it would appeal to other groups and its usage would spread.

Michael Quinion, an etymologist, researched the phrase and had this to say: http://www.worldwidewords.org/qa/qa-joe1.htm