This is similar to bug 1213694.
The Awesome Emoji Picker add-on supports all 3,000+ Unicode emojis. It also autocorrects over 130 emoticons and 1,700
:colon: shortcodes to Unicode emojis as the user types in the message body of the compose window. It is based on the open source Emoji Mart, so maybe that should be integrated into Thunderbird core so all users can have a modern and full featured emoji picker.