On Thu, 9 Nov 2017 07:55:29 -0800 (PST), Jonathan wrote:

So far as I can see the bolt has a spring around it that controls the
rocking mechanism. She has tried oiling it to no effect.

You use the word "creak", metal on metal tends to "squeak". You
really need to track down where the vibration/stiction causing the
audible creak is orginating. This may not be the same, or near, the
place the sound appears to coem from. If you have a nice long
screwdriver use it as a probe to find the real source. Place the end
of the handle against an ear and keep it there whilst you touch
various parts of the chair and listen as some one reproduces the
creak. When you find it it wil be loud and clear, further away
quieter, muffled or inaudible via the probe.

--
Cheers
Dave.