CELESTION SL6 Si - woofer replacement/repair

If you really love the speakers, you will probably need to buy another used pair, and cannibalize them for the woofers. As you probably already know, Celestion can't provide replacements, and the rubber surround was a special and integral part of the driver design. I have owned 5 versions of Celestion speakers using this woofer over the years (I still own 3 pair), and for some unknown reason, the rubber surround, while feeling soft, and otherwise looking good, can develop small fissures that almost look like they were cut with a razor knife. The speaker will still play, and doesn't sound any worse as far I as I could tell, but if it got worse over time, it would have to affect performance. I don't know if this is the problem that you are having. Anyway, it hapened to one pair that I had, and that was after I sold them to a friend. He uses them as is. It happened to another driver in one of my other pairs, but at that time, I was still able to buy a replacement.
Best thing that you can do is try to find a pair that doesn't have surround problems, and swap the driver out. They are great little speakers aren't they?

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.

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.

Lucala,
It isn't hard. First, unscrew the ribbed aluminum plate. Underneath that, the driver is screwed to the baffle. Carefully unscrew it, and you can remove the driver. It is hard wired though, so if you want to take it away from the speaker, you will need to cut or unsolder the lead wires. It is really packed with foam on the inside.