Can I color certain words in Google Document using Google Apps Script?

With the introduction of document-bound scripts, it’s now possible to make a text highlighting function that’s invoked from a custom menu.

Surely THIS is the best answer now! 8^)

This script was modified from the one in this answer, and may be called from the UI (with no parameters) or a script.

/**
 * Find all matches of target text in current document, and highlight them.
 *
 * @param {String} target     (Optional) The text or regex to search for. 
 *                            See Body.findText() for details.
 * @param {String} background (Optional) The desired highlight color.
 *                            A default orange is provided.
 */
function highlightText(target,background) {
  // If no search parameter was provided, ask for one
  if (arguments.length == 0) {
    var ui = DocumentApp.getUi();
    var result = ui.prompt('Text Highlighter',
      'Enter text to highlight:', ui.ButtonSet.OK_CANCEL);
    // Exit if user hit Cancel.
    if (result.getSelectedButton() !== ui.Button.OK) return;
    // else
    target = result.getResponseText();
  }
  var background = background || '#F3E2A9';  // default color is light orangish.
  var doc = DocumentApp.getActiveDocument();
  var bodyElement = DocumentApp.getActiveDocument().getBody();
  var searchResult = bodyElement.findText(target);

  while (searchResult !== null) {
    var thisElement = searchResult.getElement();
    var thisElementText = thisElement.asText();

    //Logger.log(url);
    thisElementText.setBackgroundColor(searchResult.getStartOffset(), searchResult.getEndOffsetInclusive(),background);

    // search for next match
    searchResult = bodyElement.findText(target, searchResult);
  }
}

/**
 * Create custom menu when document is opened.
 */
function onOpen() {
  DocumentApp.getUi().createMenu('Custom')
      .addItem('Text Highlighter', 'highlightText')

      .addToUi();
}