... the ceramics can buzz...
Don't I know it. Had to change them out for electrolytic on one of my designs. It wasn't loud, but audible, and the customer didn't like it.
Most commonly, unwanted buzzing sounds come from magnetic components - inductors and transformers. But we don't see any of those in your pictures.
The circuit on your LED board consists of a reverse-protection diode, (probably) a linear voltage regulator, and 4 strings of 3 LEDs with balancing resistors. The two caps are both on the output of the regulator. Though I can't quite make out the markings on the regulator (the largest component), it looks like a pretty reasonable design. Undoubtedly your dimmer is PWM, meaning it works by turning the LED board on and off rapidly. Leaving it on more than off makes it bright, leaving it off longer makes it dim. I'm guessing there is nothing between the dimmer and the LED board except wires?
If all that is correct and you're sure the noise is coming from the LED board, then the caps are a possible suspect. Or it could be the board itself moving from the electric fields or even thermal effects. It's pretty rare for any of these to make enough noise to be annoying (or even audible), so I'm only guessing. You might be able to learn something by poking the board while it's making the noise. If it's only a 12V or 24V system, it's quite safe to do with your fingers.
If it's the caps (small brownish parts) then you can probably only make a slight improvement by pressing on one or both of them. If it's something else, then poking at the board is likely to make a dramatic difference at some point. If you can't make any difference at all, then it's probably not actually coming from where it sounds like it's coming from. Pinning down the source of the noise will make a big difference in what solutions make sense to recommend.