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.