Just wrap them in an object literal. In pure JS (without CoffeeScript) that would be:

module.exports = {
    Page: {}, // or whatever you want to assign it to
    Serialize: {} // again, set it to what you like
};

In coffeescript you use indents, except when you want to make an empty object:

module.exports =
  Page: {},
  Serialize: {}

The problem is that required modules in NodeJS are cached. From Node's documentation:

Modules are cached after the first time they are loaded. This means (among other things) that every call to require('foo') will get exactly the same object returned, if it would resolve to the same file.

So you don't need to require the file again if you want the updated value, and you can move it outside the request callback.

You should instead export a function that returns the array, like this:

module.exports = {
  Router: router,
  artists: function () {
    return distinctArtistsArray
  }
}

and then

console.log(ArtworkSearch.artists())

You could also manually update the exported value in your code that periodically updates the distinctArtistsArray by running:

module.exports.artists = distinctArtistsArray

This needs to be done every time you update the distinctArtistsArray.

You can do something like:

module.exports = {
    method: function() {},
    otherMethod: function() {},
};

Or just:

exports.method = function() {};
exports.otherMethod = function() {};

Then in the calling script:

const myModule = require('./myModule.js');
const method = myModule.method;
const otherMethod = myModule.otherMethod;
// OR:
const {method, otherMethod} = require('./myModule.js');

// example.js
export const foods = [...
export const drinks = [...

Use the export keyword, and by not including the default keyword, your import code should work just as you submitted it.