date_picker_custom_control.php

<?php
if (class_exists('WP_Customize_Control'))
{
    /**
     * Class to create a custom date picker
     */
    class Date_Picker_Custom_control extends WP_Customize_Control
    {
          /**
           * Enqueue the styles and scripts
           */
          public function enqueue()
          {
            wp_enqueue_style( 'jquery-ui-datepicker' );
          }

          /**
           * Render the content on the theme customizer page
           */
          public function render_content()
           {

                ?>
                    <label>
                      <span class="customize-date-picker-control"><?php echo esc_html( $this->label ); ?></span>
                      <input type="date" id="<?php echo $this->id; ?>" name="<?php echo $this->id; ?>" value="<?php echo $this->value(); ?>" class="datepicker" />
                    </label>
                <?php
           }
    }
}
?>