It seems like I remember seeing or hearing about a centerdrill that has a slightly radiussed or bell shape that would be what you're looking for. I hope I'm not imagining that, but in my mind I correlated it with tapers using an offset tailstock in which the line of contact makes a slight diagonal so the bell shape is a better center than a straight 60 degree.
Ah, I'm not imagining that. MSC lists a "60 degree bell-type drill and countersink" at:
edit: Shucks, Jim beat me to it.
"In theory there’s no difference between theory and practice. In practice there’s a lot of difference.” Yogi Berra