How to draw an image over another image?

Another approach that does not require extending components.

import javax.swing.*;
import java.awt.*;
import java.awt.image.*;
import java.awt.event.ActionListener;
import java.awt.event.ActionEvent;

import java.util.Random;
import java.net.URL;
import javax.imageio.ImageIO;

public class ImageOnImage {

    ImageOnImage(final BufferedImage bg, BufferedImage fg) {
        final BufferedImage scaled = new BufferedImage(
            fg.getWidth()/2,fg.getHeight()/2,BufferedImage.TYPE_INT_RGB);
        Graphics g = scaled.getGraphics();
        g.drawImage(fg,0,0,scaled.getWidth(),scaled.getHeight(),null);
        g.dispose();

        final int xMax = bg.getWidth()-scaled.getWidth();
        final int yMax = bg.getHeight()-scaled.getHeight();

        final JLabel label = new JLabel(new ImageIcon(bg));

        ActionListener listener = new ActionListener() {

            Random random = new Random();

            public void actionPerformed(ActionEvent ae) {
                Graphics g = bg.getGraphics();
                int x = random.nextInt(xMax);
                int y = random.nextInt(yMax);

                g.drawImage( scaled, x, y, null );
                g.dispose();

                label.repaint();
            }
        };

        Timer timer = new Timer(1200, listener);
        timer.start();

        JOptionPane.showMessageDialog(null, label);
    }

    public static void main(String[] args) throws Exception {
        URL url1 = new URL("http://i.stack.imgur.com/lxthA.jpg");
        final BufferedImage image1 = ImageIO.read(url1);

        URL url2 = new URL("http://i.stack.imgur.com/OVOg3.jpg");
        final BufferedImage image2 = ImageIO.read(url2);

        //Create the frame on the event dispatching thread
        SwingUtilities.invokeLater(new Runnable(){
            @Override
            public void run() {
                new ImageOnImage(image2, image1);
            }
        });
    }
}