Botones en java

Para trabajar con un botón de esa forma debes asociar (e implementar) un manejador de eventos de ratón al botón. Te paso un programa sencillito donde se hace algo parecido.
import java.awt.FlowLayout;
import java.awt.HeadlessException;
import java.awt.event.MouseEvent;
import java.awt.event.MouseListener;
import javax.swing.JButton;
import javax.swing.JFrame;
import javax.swing.JLabel;
public class Test extends JFrame {
public Test(String title) throws HeadlessException {
super(title);
JButton button = new JButton("Press Me!");
button.setVisible(true);
JLabel label = new JLabel("Button Pressed!!");
label.setVisible(false);
getContentPane().setLayout(new FlowLayout());
getContentPane().add(button);
getContentPane().add(label);
button.addMouseListener(new ButtonAction(label));
}
private class ButtonAction implements MouseListener {
JLabel label;
public ButtonAction(JLabel label) {
super();
this.label = label;
}
public void mouseClicked(MouseEvent e) {}
public void mouseEntered(MouseEvent e) {}
public void mouseExited(MouseEvent e) {}
public void mousePressed(MouseEvent e) {
label.setVisible(true);
}
public void mouseReleased(MouseEvent e) {
label.setVisible(false);
}
}
public static void main(String args[]) {
Test test = new Test("Button Test");
test.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
test.setSize(200,100);
test.setLocationRelativeTo(null);
test.setVisible(true);
}
}