CraftCMS Push Notifications: New Device Token
I have finally figured this out with the help of the developer, boboldehampsink. Thank you so much for your help!

The post parameters are:

{
    'app': 'app_handle',
    'platform': 'ios/android',
    'registrationId': 'token'
}


Note:

You must use the front-end url to register a device without needing login credentials.

Post to the URL:
http://localhost/CraftCMS/public/actions/pushNotifications/devices/registerDevice

More information found here: https://github.com/boboldehampsink/pushnotifications/issues/1