A cup of Joe,' as a reference to a cup of coffee, first appeared as
popular slang in the 1930s and 40s. Opinions differ on where this phrase
originates from, but presented here are a few different theories.
Most sources attribute the origin of the phrase "cup of joe" to
Admiral Josephus(Joe) Daniels. Admiral Daniels was secretary of the navy
in the Wilson administration during World War I . After he outlawed
alcohol on ships, coffee becaome the favorite beverage of naval crews.
Hence the name "cup of joe."
Also on a military theme:
'A cup of Joe' also referred to the GIs' favourite drink. During World
War II the US defence workers were supplied with as much coffee as they
wanted. Coffee was a source of warmth and comfort for battle-weary
troups.
The slang was popular enough to be included in the Reserve Officer's Manual of 1931.
A variation on this theme has it that Joe refers to the average Joe,
thus making 'a cup of Joe' the average drink of the average man.
Another possible origin lies in the birth of America's taste for
coffee, which developed in the 19th century after tea was no longer
available from British merchants. The phrase may have come into the
American English language via a misunderstanding of the French word
chaud, which means "hot" and is pronounced similarly.
Finally, There was a New York company named Martinson's Coffee (Andy
Warhol liked to paint the cans) owned by a man named Joe Martinson. The
neighbourhood of the company would be saturated by the aroma of roasting
coffee, and coffee therefore became known as 'a cup of Joe'.