Stone Mugs, empty or full, do not stack. To use the Stone Mug in Brewery, just right click on a "Tapped Booze Barrel". This should fill it with the contents of the Booze Barrel unless it is empty. To use the Stone Mug in the making of Coffee, simply place the stone mug, Coffee Powder and a Water Cell or Water Bucket anywhere in the crafting table (you will get an empty bucket back, however you will not get an empty water cell back). This will make Cold Coffee. Cold Coffee is then warmed up in a furnace to make Dark Coffee. After adding a milk bucket and sugar in the crafting table similar to the way done when adding water and Coffee Beans to the Stone Mug to make the Cold Coffee, the Dark Coffee is made into genuine Coffee. Note that all stages of the Coffee are drinkable.
The Stone Mug can be crafted with coffee powder and water to make coffee.