The noise is due to excess air velocity. If the other vents in your home are quiet, you can try adjusting the dampers on the living room ducts or look for an obstruction close to the registers.

I’ve opened and closed both dampers to the living room vents . Noisy both ways . There’s no obstruction that I can see.

Density is the best sound proofing and works well to install a extra layer of sheet rock but wouldn't work for a duct. May I suggest a sound cancelling system? They sample the sound waves in the room and generate the same frequencies out of phase to cancel out the noise. They do exist.