Well... some tools to do that at your disposal.
You can copy animations from one bone to another, by copying and pasting keys in the dopesheet.
You can also duplicate animations using the Duplicate button below the Tree view.
Beyond that, 2D skeletal animation involves a lot of "cheating" (moving vertices specifically and scaling, instead of having actual 3D shapes rotate and move in the z direction) and as you've already done here. So that the program can't just do it itself. At least for now.
Other people may have tips.
[edited