I am making the assumption this is the Yamaha detach backrest ....
If so, here is something that has been done on the Raider side:
I went to the local hardware store Saturday and got 4 rubber washers. Put one on each side of bushing and used blue loctite to secure.
Then the backrest itself would rattle with a very minimal clearance issue. Went to Autozone and got some door edge guard and cut off about 1/2 inch on each strip (going to use whats left on wife's car.) and put on the backrest where it meets the bushing.
Little harder to pull off or put on, but solid as **** and no rattles
found another couple fixes:
Wrap the rear strut mounts in electrical tape. A few times around will do the trick.
Take some 4lb fishing line and create a loop. Thread it through and cut off the exposed ends. Rattle no more.