Sound deadening will work. There are a couple reasons why things rattle. Sheet metal is too light and is flexing, things are hitting each other. Find out what is happening, then go from there. Its already a given that the metal is flexing with that sub in there.

Put some weight on the big panels like the trunk lid and see if that helps. You can just kinda lean and put your weight on the trunk lid. If that helps, then you can add weight to the panels with deadening mat. Then you can do the same for the side panels and the trunk floor. After that, it might be easier to isolate the individual rattles.