Sounds a little like drilling glass, so maybe a soft core drill technique would work: obtain some steel tubing (like a hypodermic needle) and diamond paste, and core drill the hole. Now a machining center is maybe not the right machine for the job, a simple drill press with a weight hanging on the lever, while the thing runs merrily away, eroding its way in.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)