Here's a solution which uses JOptionPane to display a JPasswordField which prints blank spaces as the user types.
Really all you would want to place into your code is the showPasswordPrompt() method, but the code includes a main() method which allows you to easily test what the dialog looks like.
import java.awt.Component;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;
import javax.swing.JButton;
import javax.swing.JFrame;
import javax.swing.JOptionPane;
import javax.swing.JPasswordField;
public class JOptionPaneTest
{
    public static String showPasswordPrompt( Component parent, String title )
    {
        // create a new JPasswordField
        JPasswordField passwordField = new JPasswordField( );
        // display nothing as the user types
        passwordField.setEchoChar( ' ' );
        // set the width of the field to allow space for 20 characters
        passwordField.setColumns( 20 );
        int returnVal = JOptionPane.showConfirmDialog( parent, passwordField, title, JOptionPane.OK_CANCEL_OPTION );
        if ( returnVal == JOptionPane.OK_OPTION )
        {
            // there's a reason getPassword() returns a char[], but we ignore this for now...
            // see: http://stackoverflow.com/questions/8881291/why-is-char-preferred-over-string-for-passwords
            return new String( passwordField.getPassword( ) );
        }
        else
        {
            return null;
        }
    }
    public static void main( String[] args )
    {
        final JFrame frame = new JFrame( );
        final JButton button = new JButton( "Push Me For Dialog Box" );
        button.addActionListener( new ActionListener( )
        {
            @Override
            public void actionPerformed( ActionEvent e )
            {
                String password = showPasswordPrompt( frame, "Enter Password:" );
                button.setText( password );
            }
        } );
        frame.add( button );
        frame.setSize( 400, 400 );
        frame.setVisible( true );
    }
}