I have been successful in managing contact groups with OS X's Contacts.app and iCloud.com, but haven't found a way to do this as of iOS 9.
Is there a way to manage contact groups on iOS (iPhone, iPad, or iPod Touch) ?
Ask Different is a question and answer site for power users of Apple hardware and software. It only takes a minute to sign up.Sign up to join this community
No, there is no way to create or edit contact groups on iOS. I share your frustration! The best workaround is to use iCloud.com (or your primary Mac, if you have it with you).
Also, there is a way to add contacts to a specific group on iOS, though it's not obvious:
+) in the top right
Now when you create and save the contact, it'll save it in that specific group. You can then go back to the Groups list and reenable all your groups.