Custom field options are set by administrators.
Project owners can be given maintenance of Components, Versions and Users. That's all. Atlassian are working on a more flexible model, but it's not there yet.
I don't think it is a good idea unless it also locks the field from being used by another project or a particular context version of the field can be managed. Otherwise there is too big a chance someone will delete a value being used by another project. especially since the documentation says there is no warning the value is in use when deleting like there is with the build in editor.
I've got the same worry.
Part of it is experience - almost every Jira site I've been to has started with a project to clean up the mess made by allowing too many administrators. You'll generally find that project leads are ok when limited to their own project (like components and versions) but they will make a total mess of shared fields. I really wouldn't install anything like that!
You can't do this because only a JIRA admin can change the custom field options. You will be able to write a plugin to do this, if needed, but remember that the custom fields might be shared between projects.
Hey Support - Just wanted to chime in here about a plugin I ran across in the 'free' section on a local 6.3.1 install. It claims to allow you to delegate permission to users/groups to update the values in a custom field. I just set it all up last night so I'm not sure how well it works, or even how it works, but it is a feature long time missing from JIRA. Here's the name and URL: Jira Customfield Editor Plugin
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