Tip needed - resonating

My DIY sub design is pretty good, but if you go too loud (and not *that* loud), the bracket that holds the voice coil starts rattling a little, and indeed I think there is a tiny bit of space somewhere.

Is there some fix recommendation for it, or is it 'start over'?

For example: is there some recommended sheet of maybe compressable rubbery material I can just squeeze into the gap and hope it'll stop the final bit of vibration?
Is this what you call "a bracket"?
It´s commonly called a "spider" or "suspension".


There must be a bead/ring of adhesive joining it to the voice coil and cone, typically epoxy, although on the "outside" (what you can see through frame holes) you may use some kind of white PVA "carpentr´s glue" since you would be bonding cloth to paper and the outside does not get hot; and the outer edge is glued to speaker frame with PVA or contact cement.

Just carefully reglue what became loose, apply what´s needed with a brochette stick, kind of an oversized toothpick, but don´t make a mess of it and avoid spilling adhesive inside the voice coil gap .
Sorry I think I misrepresented the problem a bit.

The Driver is fine. It's screwed down well into the front of the cabinet, but when going louder I think the 'magnet' part of the driver (I think I confusingly called it the 'voice coil') rattles around in the cabinet brace because it's not put in there tightly enough.

To form the image - here's a picture (of a different design)

Subwoofer Cabinet

I think the magnet part, rear of the driver is rattling around in the 'light wooden square' in the center of the cabinet.

I'm suggesting I might just put some rubbery material across that brace where pushing the driver into the cabinet (and screwing it down in the front), the magnet would be pushed against that material in the back?