Currently the REST API supports the GET method on api/2/customFieldOption/

With support of PUT (or POST) operation on that URI additional workflows would be supported.

Use Case: a system manages some mostly automatic process. When manual intervention is required the system opens an issue in Jira. Ticket resolution includes assigning a value to a field, accomplished via a Jira Custom Field. The domain of options, however, is managed by the system and any selected option must be valid within that domain. Since the system is used to add options to itself - stored in a database table - to ensure the automated parts and the Jira workflow parts work well together the sets of possible options need to stay in-sync. As part of its processing the system can create new option values within itself. Adding the ability to PUT/POST the Jira custom field option values would ensure data integrity and consistency across the automated and more manual, Jira-driven parts of the workflow.

As for needs, either a simple PUT with the full set of option values included in the request, or the ability to add and delete individual option items would work.