I used some stuff many years ago that I believe was called "chair-lok".
It came in a little squeeze bottle. They claimed that it would swell
the wood to make a tight joint. I seem to also remember using some
little corrugated metal strips that you put in the hole before you jam
in the "plug". The hardest part was doing a good clamping job, since
none of the legs on these Windsor style chairs were parallel, nor did
the struts meet the legs at right angles.

Now if I could only remember if all that worked worth a damn I'd have
some good advice to give you. It was a long time ago and those
chairs are long gone.

Greg Guarino