There is no legal "standard" coffee cup; although the most correct answer could be either 5 fluid ounces [for home brewed coffee], 5-1/3 fluid ounces [restaurant coffee] or 6 fluid ounces [of cold water]. Most table settings come with cups that hold approximately 6-9 fluid oz.
The SCAA defines the gold standard for a cup of coffee as 6oz of cold water resulting in about 5-1/3 fluid oz of brewed coffee (some water loss due to evaporation and absorption by coffee grounds). Most manufacturers of home brewers in the United States round this off to 5 oz for marketing purposes so that a 50 oz pot is sold as a 10 cup carafe. If a coffee maker is marked with measurements in cups on the side it usually indicate 5 fluid ounces for each cup. Commercial (ie, Restaurant) brewers generally use a "12 cup" carafe that holds 64 ounces of brewed coffee resulting in 5-1/3 ounces per cup.
Coffee makers and distributors in the United States refer to a "standard serving" of coffee as 6 fluid oz of cold water (the term "cup" is not used on the typical coffee can/package/box sold in a supermarket). This can result in a slight overfilling of home coffee makers since a "serving" of coffee (as defined by coffee producers) is usually a fraction of an ounce larger then the typical "cup" (as defined by coffee brewer manufacturers).
Specialty coffees such as expresso, french press makers, etc, sometimes use other sizes.