Emoticons and emoji replacements can be managed by going to Administration > Site > Emoticons:
Emoticons are grouped into categories. Each category contains one or more emoticons which can have variations (for skin tone, for example, as is the case with emoji). A new collection can be added by clicking Add Collection. Existing collections can be edited by selecting the collection and clicking Edit. Selected collections can also be moved up/down to order the collections when listed within the content editor.
When editing a collection, emoticons can be edited by clicking the emoticon from the list and new emoticons can be added by clicking Add Emoticon.
The default categories mirror the groupings of emoji characters which are part of Unicode. Emoticons and emoticon categories that relate to emoji/Unicode can be enabled/disabled but cannot be removed. Disabling a category or a single emoticon within a category related to emoji disables that emoji character from being used in any content within the community. Enabled emoticons related to emoji will replace the emoji character to provide a consistent visual representation of the emoji for all members of the community.