There is a JComponent.setComponentPopupMenu() method wich allows you to set a popup for this particular component, the problem is that it doesn't support different popups for different parts of the component.

It is proposed to add a new method
JComponent.getComponentPopupMenu(MouseEvent event)
which you can override and return the popup for the particular coordiantes

The same approach as getToolTipText(MouseEvent event) is implemented