I am often in need of some emojis when committing on my github repos. As I don't have an always on Internet connection, I had to sacrifice them when I was not online. I tried saving the http://emoji.muan.co/ page but that didn't work. So I wrote a simple Python script to set up a server from the emoji's directory and run the browser with the emoji selector running on localhost.
You can find the script at https://github.com/aviaryan/pythons/tree/master/EmojiServer. The instructions in README should be sufficient to set it up and start using it.