You could use a simple JPanel instead of extendint it.
What's the point in extendint it?

Try this:
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import javax.swing.*;
import java.awt.*;

public class IMIEasternButtonPanel extends JPanel {
 private JButton m_btnUp, m_btnDown;

 public IMIEasternButtonPanel(){
   setLayout(new BoxLayout(this, BoxLayout.Y_AXIS));
   setPreferredSize(new Dimension(500,50));
   addChilds();
 }

 public void addChilds(){
   m_btnUp = new JButton(new ImageIcon("up.gif"));
   m_btnUp.setMinimumSize(new Dimension(50, 50));
   m_btnUp.setMaximumSize(new Dimension(50, 50));
   m_btnUp.setPreferredSize(new Dimension(50, 50));
   add(m_btnUp);
 }

 public static void main(String[] args){
   JFrame frame = new JFrame();
   frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
   IMIEasternButtonPanel iebp = new IMIEasternButtonPanel();
   frame.getContentPane().add(iebp, BorderLayout.EAST);

   frame.setSize(500, 500);
   frame.setVisible(true);
 }
}