Since the default cloud function for Dialogflow ES does not work anymore, I have created a minor modification that allows one to run it directly from your agent

index.js

// See https://github.com/dialogflow/dialogflow-fulfillment-nodejs
// for Dialogflow fulfillment library docs, samples, and to report issues
'use strict';
 
const functions = require('firebase-functions');
const {WebhookClient} = require('dialogflow-fulfillment');
const {Card, Suggestion} = require('dialogflow-fulfillment');
 
process.env.DEBUG = 'dialogflow:debug'; // enables lib debugging statements
 
exports.dialogflowFirebaseFulfillment = functions.https.onRequest((request, response) => {
  const agent = new WebhookClient({ request, response });
  console.log('Dialogflow Request headers: ' + JSON.stringify(request.headers));
  console.log('Dialogflow Request body: ' + JSON.stringify(request.body));
 
  function welcome(agent) {
    console.log(JSON.stringify(agent,null,2));
    agent.add(`Welcome to my agent!`);
  }
 
  function fallback(agent) {
    agent.add(`I didn't understand`);
    agent.add(`I'm sorry, can you try again?`);
  }

  // // Uncomment and edit to make your own intent handler
  // // uncomment `intentMap.set('your intent name here', yourFunctionHandler);`
  // // below to get this function to be run when a Dialogflow intent is matched
  // function yourFunctionHandler(agent) {
  //   agent.add(`This message is from Dialogflow's Cloud Functions for Firebase editor!`);
  //   agent.add(new Card({
  //       title: `Title: this is a card title`,
  //       imageUrl: 'https://developers.google.com/actions/images/badges/XPM_BADGING_GoogleAssistant_VER.png',
  //       text: `This is the body text of a card.  You can even use line\n  breaks and emoji! 💁`,
  //       buttonText: 'This is a button',
  //       buttonUrl: 'https://assistant.google.com/'
  //     })
  //   );
  //   agent.add(new Suggestion(`Quick Reply`));
  //   agent.add(new Suggestion(`Suggestion`));
  //   agent.setContext({ name: 'weather', lifespan: 2, parameters: { city: 'Rome' }});
  // }

  // // Uncomment and edit to make your own Google Assistant intent handler
  // // uncomment `intentMap.set('your intent name here', googleAssistantHandler);`
  // // below to get this function to be run when a Dialogflow intent is matched
  // function googleAssistantHandler(agent) {
  //   let conv = agent.conv(); // Get Actions on Google library conv instance
  //   conv.ask('Hello from the Actions on Google client library!') // Use Actions on Google library
  //   agent.add(conv); // Add Actions on Google library responses to your agent's response
  // }
  // // See https://github.com/dialogflow/fulfillment-actions-library-nodejs
  // // for a complete Dialogflow fulfillment library Actions on Google client library v2 integration sample

  // Run the proper function handler based on the matched Dialogflow intent name
  let intentMap = new Map();
  intentMap.set('Default Welcome Intent', welcome);
  intentMap.set('Default Fallback Intent', fallback);
  // intentMap.set('your intent name here', yourFunctionHandler);
  // intentMap.set('your intent name here', googleAssistantHandler);
  agent.handleRequest(intentMap);
});

package.json

{
  "name": "dialogflowFirebaseFulfillment",
  "description": "This is the default fulfillment for a Dialogflow agents using Cloud Functions for Firebase",
  "version": "0.0.1",
  "private": true,
  "license": "Apache Version 2.0",
  "author": "Google Inc.",
  "engines": {
    "node": "10"
  },
  "scripts": {
    "start": "firebase serve --only functions:dialogflowFirebaseFulfillment",
    "deploy": "firebase deploy --only functions:dialogflowFirebaseFulfillment"
  },
  "dependencies": {
    "actions-on-google": "^2.2.0",
    "firebase-admin": "^5.13.1",
    "firebase-functions": "^2.0.2",
    "dialogflow": "^0.6.0",
    "dialogflow-fulfillment": "^0.5.0"
  }
}