Well, I'm don't use GridBagLayout much but I think you need to use the "anchor" constraint with a value "CENTER. Read the section from the Swing tutorial on How to Use GridBagLayout for a better description of the contraints.
Or, another option is to add the scrollpane containing the table to the CENTER of the BorderLayout. Then you create a JPanelm, which by default uses a FlowLayout. You add your button to this panel and then add the panel to the BorderLayout.SOUTH.