For a century, the executives of Coca-Cola Co. have done everything possible to put their famed cola "within arm's reach of desire," to the point that one chief executive frequently pondered an extra tap at the kitchen sink—with Coke flowing from it. The company's plan to team up with the maker of the Keurig single-serve coffee brewers to develop a do-it-yourself countertop Coke machine comes pretty close. The new cold drink machine won't look anything like SodaStream, the leading home soda maker, says Coke's new partner, Green Mountain Coffee Roasters Inc. It will have a similar design to Green Mountain's...