This is an example of my solution for installing a standalone version of Node.js on a Raspberry Pi in support of a larger project.
I created a Debian package for my Node.js service, and wrote a post-install script that installed a standalone Node version when the Debian package was installed. I also included a systemd service file to run the service and to restart it in case it crashes. This repository contains a sample of this technique. Feel free to grab it and use it as a model for your own Node.js services if you desire.
If you want a full explanation of what this sample contains, see my write up on carpie.net.