As was mentioned, iron stacks are in theory quieter than PVC. It's stiff and has mass, much like it makes for good engine blocks, it does have nice properties for drain stacks. My house had an iron stack, it's gone now, and maybe the PVC is louder, but doesn't matter, it will be packaged in walls in time with sound insulation around it. Not corroding and clogging is more important. It's pretty impressive when you snap the stack and see how good inside 60 year old iron can look inside, but still, the corrosion is there, spots get thing, crud builds up. PVC avoids this. If you want to see nasty, it's the line off a kitchen sink, kitchen sink + iron = no good, of course getting garbage disposers banned and teaching people sinks are not universal waste disposal ports is a key to fix these issues.
I can't image your P-trap in plastic is any worse than brass far as noise. It could be more of the geometry of your routing causing some odd flow thru it. Stick with PVC, avoid sudden failures.
I would avoid the temptation to coat the PVC with anything, my concern is what you apply may have a reaction to the PVC and in time cause a failure. Creating an unknown. Also it might make spotting a leak harder.
I think I have seen some formed wraps for going around P-traps. I think these are a bit for looks and to avoid condensation. The would probably have some noise benefit.
