Implements HOOK_html_head_alter() in the theme so that output from http://realfavicongenerator.net/ can be downloaded, extracted into the theme's assets folder. http://www.drupalcontrib.org/api/drupal/drupal!core!modules!system!system.api.php/function/hook_html_head_alter/8

theme_head-tags_favicons.inc

<?php

/**
 * Implements hook_html_head_alter().
 *
 * @param array $head_elements
 */
function THEME_html_head_alter(&$head_elements) {
  // Loop through $head_elements array, find link tag that matches core default
  // favicon implementaiton override meta data to point to new iconography file.
  foreach ($head_elements as $key => $element) {
    if ( 0 === strpos($key, 'drupal_add_html_head_link:shortcut icon:')
      && !empty($element['#attributes']['href'])
      && 'shortcut icon' === $element['#attributes']['rel']
    ) {
      // Make sure to use a file that actually exists!
      $favicon_path = drupal_get_path('theme', 'THEMENAME') . '/assets/favicons/favicon.ico';
      $favicon_url = file_create_url($favicon_path);
      // If the favicon path came from a user-provided setting, we would also need drupal_strip_dangerous_protocols().
      $element['#attributes']['href'] = $favicon_url;
      $element['#attributes']['type'] = 'image/vnd.microsoft.icon';
      $head_elements[$key] = $element;
    }
  };

  // Create arrays for favicons that follow similar conventions.
  $apple_touch_icon_sizes = array(
    '57x57',
    '60x60',
    '72x72',
    '76x76',
    '114x114',
    '120x120',
    '144x144',
    '152x152',
    '180x180'
  );

  $general_favicon_sizes = array(
    '16x16',
    '32x32',
    '96x96',
    '194x194'
  );

  // Add Apple touch interface icons
  foreach ($apple_touch_icon_sizes as $icon_size) {

    $head_elements['drupal_add_html_head_link:apple-touch-icon_' . $icon_size] = array(
      '#type' => 'html_tag',
      '#tag' => 'link',
      '#attributes' => array(
        'rel' => 'apple-touch-icon',
        'sizes' => $icon_size,
        'href' => drupal_get_path('theme', 'THEMENAME') . '/assets/favicons/apple-touch-icon-' . $icon_size . '.png'
      ),
      '#weight' => -9999
    );

  };

  // Add fallback for versions of iOS less than version 7
  $head_elements['drupal_add_html_head_link:apple-touch-icon-precomposed'] = array(
    '#type' => 'html_tag',
    '#tag' => 'link',
    '#attributes' => array(
      'rel' => 'apple-touch-icon-precomposed',
      'href' => drupal_get_path('theme', 'THEMENAME') . '/assets/favicons/apple-touch-icon-precomposed.png'
    ),
    '#weight' => -9998
  );

  $head_elements['drupal_add_html_head_link:apple-touch-icon-fallback'] = array(
    '#type' => 'html_tag',
    '#tag' => 'link',
    '#attributes' => array(
      'rel' => 'apple-touch-icon',
      'href' => drupal_get_path('theme', 'THEMENAME') . '/assets/favicons/apple-touch-icon.png'
    ),
    '#weight' => -9997
  );

  // Add Safari browser icon for pinned tabs
  $head_elements['drupal_add_html_head_link:safari-pinned-tab'] = array(
    '#type' => 'html_tag',
    '#tag' => 'link',
    '#attributes' => array(
      'rel' => 'mask-icon',
      'href' => drupal_get_path('theme', 'THEMENAME') . '/assets/favicons/safari-pinned-tab.svg',
      'color' => '#018dc7'
    ),
    '#weight' => -9996
  );

  // Add icons for Chrome, Firefox and other browsers
  foreach ($general_favicon_sizes as $icon_size) {

    $head_elements['drupal_add_html_head_link:favicon_' . $icon_size] = array(
      '#type' => 'html_tag',
      '#tag' => 'link',
      '#attributes' => array(
        'rel' => 'icon',
        'sizes' => $icon_size,
        'type' => 'image/png',
        'href' => drupal_get_path('theme', 'THEMENAME') . '/assets/favicons/favicon-' . $icon_size . '.png'
      ),
      '#weight' => -9995
    );

  };

  // Add Android specific link tag for favicon image and meta tag for theme-color.
  $head_elements['drupal_add_html_head_link:android-chrome_192x192'] = array(
    '#type' => 'html_tag',
    '#tag' => 'link',
    '#attributes' => array(
      'rel' => 'icon',
      'sizes' => '192x192',
      'type' => 'image/png',
      'href' => drupal_get_path('theme', 'THEMENAME') . '/assets/favicons/android-chrome-192x192.png'
    ),
    '#weight' => -9994
  );

  $head_elements['drupal_add_html_head_meta:android-theme-color'] = array(
    '#type' => 'html_tag',
    '#tag' => 'meta',
    '#attributes' => array(
      'name' => 'theme-color',
      'content' => '#018dc7'
    ),
    '#weight' => -9993
  );

  // Add manifest file for future-proofing when web-apps become a _thing_
  // recognized by all browsers in all OSs, not just Android.
  $head_elements['drupal_add_html_head_link:web-app-manifest'] = array(
    '#type' => 'html_tag',
    '#tag' => 'link',
    '#attributes' => array(
      'rel' => 'manifest',
      'href' => drupal_get_path('theme', 'THEMENAME') . '/assets/favicons/manifest.json'
    ),
    '#weight' => -9992
  );

  // Add Microsoft specific favicon images, primarily used for bookmarks and
  // tiles added to the system start menu.
  $head_elements['drupal_add_html_head_meta:msapplication-TileColor'] = array(
    '#type' => 'html_tag',
    '#tag' => 'meta',
    '#attributes' => array(
      'name' => 'msapplication-TileColor',
      'content' => '#018dc7'
    ),
    '#weight' => -9991
  );

  $head_elements['drupal_add_html_head_meta:msapplication-TileImage'] = array(
    '#type' => 'html_tag',
    '#tag' => 'meta',
    '#attributes' => array(
      'name' => 'msapplication-TileImage',
      'content' => drupal_get_path('theme', 'THEMENAME') . '/assets/favicons/mstile-144x144.png'
    ),
    '#weight' => -9990
  );

  // Add the config file that tells Windows what to do with the previously
  // defined meta tags.
  $head_elements['drupal_add_html_head_meta:msapplication-config'] = array(
    '#type' => 'html_tag',
    '#tag' => 'meta',
    '#attributes' => array(
      'name' => 'msapplication-config',
      'content' => drupal_get_path('theme', 'THEMENAME') . '/assets/favicons/browserconfig.xml'
    ),
    '#weight' => -9989
  );
}