There are a bunch of drill/countersink combinations available. Most have one size drill bit that usually can be adjusted. You need a set to cover the typical ranges used in woodworking. Some drills are tapered, some are not.
I found an interesting tool called "Coopers Countersink Drill Chuck". At a glance it looks like a common three jawed chuck. Looking closer the three jaws are sharpened into cutters. The chuck also has a hollow spindle allowing drill bits to be adjusted for depth. The hollow allows up to a 5/16" bit to be used. While the shaft is round, it can be used in either a drill press or a brace that can handle round shafts. This chuck was invented by Hugh H. Cooper of Troy, New York and is patent #1,294,054 (Feb. 11, 1919). Bored a hole and countersunk in walnut with a brace. Works very well.
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