Of course, there’s always the proper engineering method … using a
drilling bush.
Take some hardenable steel rod (“silver steel” here in the UK, “drill
rod” in other places) exactly the same diameter as the ball, and cut a
length about twice as long as the ball diameter. Get the ends nicely
square to the length. Drill right through, to finish with a hole a
nice sliding fit for the drill you will be using. It may be necessary
to start off with a smaller drill (all the way through), and use the
finish size drill to just bring the hole to correct size. Lightly
contersink one end, and deeply countersink the other. Ideally it
should now be hardened and tempered.
Put the ball in you drill vice, with the bush on top, vertical, with
the deep countersink resting on the ball. Use solid packing under the
ball if necessary to raise it. You have to arrange for the bush to be
vertical in the vice, and directly underneath the drill bit in the
drill press, which may be a bit fiddly the first time, but once the
vice is in the correct position clamp it in place (should do that
always anyway). Since the bush and ball are the same diameter they
should both be held firmily by the vice jaws, but it doesn’t hurt to
put a thin piece of paper or shim stock between them and the vice jaw.
The drill is now perfectly guided, dead on centre, no need to use a
slocumbe. Just remember that now you are drilling, in effect, at the
bottom of a rather deep hole, so raise the drill rather frequently to
clear swarf, use a lubricant, and don’t let the drill rub on the
stainless. Good luck! – Kevin (NW England, UK)