CELESTION SL6 Si - woofer replacement/repair

I didn't really think you would find one speaker, I was talking about buying a pair. They come up cheap enough to make it worthwhile if you really like them.
They aren't my primary speakers either, but they just have really great balance of performance virtues that makes music sound good, and makes you forget what they can't do.

You might be able to find someone to re-cone speakers with butyl surrounds. (Re-coning doesn't necessarily have to mean replacing the cone assembly-it can involve voice-coils and surrounds also).
I'm no chemist but I've noticed some white residue that seems to build up with these butyl rubber surrounds. I've been wiping it off with a damp cloth, and following that with an Armor-all treatment. And crossing my fingers. BUT, I believe that Armor-all has silicone, so keep it away from the woodwork,it can make refinishing very difficult (fisheyes lacquer) also could make touch-ups tricky too.

Have you tried to tighten the screws or bolts holding the woofers in place. Almost all woofers get loose eventually and need to be tightened up. The noise you're hearing is typical of the loose woofers.
Do NOT try to tighten them down hard.
Just tighten them down snug.
And if it IS the woofer, then recone the woofer, not get a new speaker. Reconing shops all over the place can do the speaker and replace the surround and or recone the speaker. Get both done at one time if reconing.

Give Bill Legall from Millersound a call to get his opinion on this situation;he is well known in the business and highly respected for his work.

Millersound
1422 Taylor Road
Lansdale, PA 19446-1531
(215) 412-7700

If you have owned the SL series of Celestion speakers, you will know that these can't be reconed or have the surrounds replaced. The driver was proprietary to Celestion. It was unique in not having a dust cap (which was unusual at that time), and changing it for a different driver would no doubt change the sound of the speaker completely.
Elizabeth's comment is a good one. These drivers need to be checked for tightness on a regular basis. Also check the ribbed aluminum diffraction plates around the drivers for tightness.
You didn't say if you had found any cracks in the surround. If you have, and that turns out to be what is causing the buzzing that you hear, I think that the only alternative will be finding a used driver.