I have added cobblestone for the granite, andesite and diorite variants. Now I want to be able to make them get dropped by their corresponding blocks.

How (and where) can I overwrite the BlockStone's getItemDropped method?

You can't override methods from vanilla classes. Instead you should use events - in this case,

HarvestDropsEvent

. In the event handler method, you can check whether the block is granite/andesite/diorite, and edit the list of drops to remove the vanilla block and add your cobblestone version.