The exact liquid measurement of a "cup" as noted on the side of a coffee maker is subjective since there is no industry wide standard unit of measure. Lee Denny explains this in his article:
One thing is for sure: a "cup" of coffee does not fill up the typical 12 oz. coffee mug found in most American homes.
Ounces per Cup in Popular Coffee Maker Brands
Bunn: 5 oz
Bodum (Vacuum): 5.7 oz
Capresso: 5 oz
Cona: 5.5 oz to 5.7 oz
Cuisinart: 5 oz
Krups: 5 oz
Proctor Silex: 4.5 oz
Technivorm: 4.2 oz
Zojirushi: 5.1 oz
To complicate things even further, coffee brewing instructions frequently tell you how much ground coffee to add for every 6 ounces of water. You'll see this metric on the back of a can of Maxwell House as well as published by coffee authorities such as the National Coffee Association of U.S.A., Inc. Further proof of the lack of standardization.
That being said, neither is their an internationally recognized standard measure for what a "cup" is since American uses cup measurements while many other countries use kitchen scales to mete out ingredients by weight. This entertaining article Sue Quinn wrote for The Telegraph explores this difference:
Here in the UK, we love your food, we really do. We guzzle your dirty burgers, crave your Cronuts and scoff your hot dogs like there’s no tomorrow. But your recipes are giving us heartburn. Why on earth do your cookbooks and food websites cling to cup measures when kitchen scales are much easier, more precise and infinitely less faff?
Quinn provides an excellent cups - metric weight guide if you are interested in eliminating the cup conundrum by buying a kitchen scale for use going forward. If you do make the switch to weights, then try the National Coffee Association's recipe:
A general guideline is one to two tablespoons of ground coffee for every six ounces of water. This can be adjusted to suit individual taste preferences.
Be sure to check the “cup” lines on your brewer to see how they actually measure. And remember that some water is lost to evaporation in certain brewing methods.
If you are still interested in pursuing cup measurement, it may interest you to know that Fannie Farmer is given much credit for establishing the American way of measuring ingredients as noted by Bill Daily in this Chicago Tribune article:
Fannie Merritt Farmer was an influential New England cooking teacher with a flair for marketing and promotion whose 1896 "The Boston Cooking-School Cook Book" and myriad subsequent editions have made her a household name for more than a century.
Often called the "mother of level measurements" for her insistence on the use of measuring cups and spoons in cooking and in recipes, Farmer shaped the appetites of a nation through her cookbook.
If you want an up close and personal look at how Farmer popularized the use of the cup measurement system, check out her cookbook here at Internet Archive.