I am writing an application where the user can change the color of the image on screen by choosing a new color.  I have a simple image - only 40x40 - like this:

I have tried many things: pixel replacement, ColorModel, RGBFilter, etc. I can't figure this image stuff out. In the process of trying, I have learned about BufferedImage and I can get the .png's into that format and displayed on screen. I can turn the shape into a solid blob of color using pixel replacement, but the results are horrible.
From what I've gleaned, I want to use a ColorModel or Filter, but I am stumped. Here is a simple app that demonstrates where I am.
import java.awt.BorderLayout;
import java.awt.Color;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;
import javax.swing.ImageIcon;
import javax.swing.JButton;
import javax.swing.JColorChooser;
import javax.swing.JFrame;
import javax.swing.JLabel;
public class ChangeImageColor {
  public static void main(String[] args) {
    final ChangeColor cc = new ChangeColor();
    java.awt.EventQueue.invokeLater( new Runnable() { @Override
      public void run() { cc.setVisible( true ); }}
    ); // invokeLater
  } // main
} // ChangeImageColor
  class ChangeColor extends JFrame {
    String  CHAR_HEAD    = "res/images/char/Head.png";
    JLabel  imageHead    = new JLabel( new ImageIcon( CHAR_HEAD ) );
    JButton buttonChoose = new JButton( "Choose Color" );
    public ChangeColor() {
      this.setSize( 200, 200 );
      this.setLayout( new BorderLayout() );
      buttonChoose.addActionListener( listenerButton );
      this.add( imageHead, BorderLayout.CENTER );
      this.add( buttonChoose, BorderLayout.SOUTH );
    } // constructor
    ActionListener listenerButton = new ActionListener() {
      @Override public void actionPerformed( ActionEvent event ) {
        Color newColor = JColorChooser.showDialog( null, "Choose Color", Color.RED );
        ImageIcon icon = new ImageIcon( CHAR_HEAD );
        System.out.println( "~" + newColor );
        // *****************
        // insert code to change color of Head.png to shades of chosen color
        // *****************
        imageHead.setIcon( icon );
      } // actionPerformed
    };
  } // class
(I've never worked with dynamic colors and images, so I'm way over my head. Thanks in advance for your help.)
Edit: Here is a "before" and "after" image of what I would like after a darker color is chosen:
