I am a goldsmith in the UK and I often have to find the centre of
discs. The first thing you must buy yourself is a disc centre lining
tool, they are not expensive probably only a few dollars, they are
even easy to make for yourself. They are steel and consist of a right
angle with a straight edge disecting the right angle so that you can
scribe a line disecting the disc, and by turning the disc around and
scribing a second line you have a dead centre where the line cross. I
could send you a photo of my centering tool if you want. My second
suggestion is for you to make a marking jig, I have made these type
of jigs to speed up production when needed. Jig making method as
1) cut a square of base metal ( copper or brass ) slightly thinner
than the disc thickness,then pierce out a perfect fit cavity circle
for your disc size in the square centre.
2) rivet the square base metal to a smae size piece of thin tool
steel ( rivet in each corner ).
3) do the geometry and find the centre of one disc, place in cavity
and drill a hole in the steel
4) anneal the whole jig and drop in water when dull red hot, this
will harden the steel.
5) clean up and you have a jig that discs will fit into while you
can mark dead centre with your pendant drill.
Please let me know if you would like detailed sketches.
I hope this all make sense, good luck, regards James
see my work here if you are interested