We alodined ours. Just take a little acid brush and dip it in Alodine, then put a drop in the countersink. Surface tension will hold the drop there, completely filling the hole/countersink...you can do a couple dozen, let them sit for a bit, then wipe down with a wet paper towel and blow dry. Looks nice, quick and easy, and no need to mess with paint (also avoids the loss of countersink depth due to paint thickness).
Just another option...
Steve