Ken C. has a good method for making the washers, however I take a bit of a different approach.
The vast majority of my shadow knives are either G10 or Micarta so I am working with a material that is flat. I start by building my frames(.040 thick 410) with all holes drilled(3/32) then gluing up the scale material. I use 1/4 410 rod for my birdseye's rivets. After the scale is glued and set, I drill my 3/32 holes thur the scale material, using the liner as the drill jig. I then will flip the scale/frame over on the drill press and using the 3/32 hole as a guide, drill in steps up to 1/4 inch. I have a 1/4 inch drill that I ground a very shallow point on. I will leave just a bit of scale material at the bottom of the hole. I want the washer to pinch the scale to the liner when I do my final assembly. I now have a 1/4 inch counter bore centered on my 3/32 pivot pin hole. I simply cut a piece of 1/4 rod, epoxy it in the hole, grind it flush(keeping it cool) and then flip the scale over again on the drill press and drill through with my 3/32 drill. The last step is to taper the hole with a 2 degree taper reamer. You can then contour the scales/birdseye rivet. The beauty of this(imho) method is that it does not require a lathe, counter bore or special tools. Really does take longer to type and read this, then to do both sides!