Try deactivating and reactivating the plugin. That role is created during the activation process, so perhaps it didn’t get created initially for some reason, or it somehow got deleted.
It’s not any kind of option in the plugin settings, it’s a user role that mimics that “author” role of WordPress, but adds the capability to also manage sign-up sheets. So, you have to go to the Users section in the admin dashboard, edit a user, and assign that role to them.
If you don’t want the user to have the other capabilities that the author role has, or you want to give some other role the capability to manage signup sheets, then you need to use one of the free role/capability manager plugins and add the capability to the specific user (or other role) that you want to be able to do that. The name of the capability to add is simply: manage_signup_sheets