Locating A Part To Be Drilled On Center. ?

Speedy way? Chuck up a dowel pin. Lower it below the edge centerline of your round stock and hold a flashlight behind it. Ease the work piece over until you see the dowel pin touch. If you don't have DRO's, move toward center half the dowel diameter, and then continue moving half the work piece diameter. This will get you within .002 or .003" in most cases. If you do have DRO's, touch off on one side and zero the axis you're moving in. Touch off on the other side and then divide your readout number in half.

The absolute best way I've ever found for centering, short of bringing lasers into play, is the IndiCol attachment and a test indicator. You can center a hole to within .00002" if you have the correct indicator and the patience to work at that level. Choose your method based on the required tolerance of the job at hand.
 
An XY table with an edge finder would be the most accurate. I've used this little gizmo for non critical cross holes.

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I use one of those for drill press work. Works just fine for what I need to get done.

You did say you have a basic drill press with no X Y capability and I think the gizmo is fast and easy for that.
 
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