A tip to establish a center line starts back when the ball is placed in the template. (See the post on Opening a Golf Ball) The cardboard is positioned perpendicular to the brand name printed on the ball with one complete brand name showing on each side of the template. Notice the pencil line on the template to aid in positioning the brand name. After the cover has been removed, it’s easy to continue the imaginary brand line around to the exposed rubber.
I make a small reference line on the rubber to indicate the middle of the brand line on both (and opposite) sides. (Click on image to enlarge.)
Adjust a compass, that uses an ink pen, so it reaches from one cover edge where you just made a reference mark to your best guess at the center. Make a small mark there.
Without adjusting it, move the compass to the reference mark on the other side and check to see how good your center guess was. If you are lucky, or just very good at guessing, the pen will land on the first center mark.
Otherwise, adjust the compass to split the difference between the two center measurements and draw a complete line from “top” to “bottom” on the rubber.
It’s important to reposition the compass at the other reference mark and draw a “top” to “bottom” line from that side, too. Rarely do the two lines match perfectly but you now have a center reference.