I have an old set of CODA SPD pedals that I am trying to grease the bearings. How do I adjusted the bearings? The cone turns when I try and tighten the locking nut preventing me from being able to get the proper preload on the bearings.

try using a pick or a small screwdriver to hold the cone as you turn the locking nut.

I tried using a small screwdriver but was unable to hold the adjusting cone.

I had the same problem last week. There is a Shimano tool that will hold the cone as you adjust the wrench. I was able to order one through my LBS and it's due in "late this week." It was surprisingly inexpensive.
Did you replace the bearings? What size would I ask for?

from what I read the shimano tool is 11mm cone and 8mm locking nut. My pedals are 11mm cone and 9mm locking nut. I did not replace the bearings they were in surprising good condition.