Ryuhei Yokokawa

Plugin will allow you to fetch the WP-API (WP-JSON-API) call with a “lang” variable. It will retrieve the right content from WPML/WP.
This only works with WPML and WP-API installed. I tested only with the latest version as of now: 
* WPML 3.1.9.6 
* WP REST API 1.2.1

WPML to WP API

Allows you to request a language with your WP-API and WPML site.

Ali Qureshi

JSON API Cincopa plugin extends the JSON API Plugin with a new Controller to provide Cincopa Easy Albums Listing for any user. This plugin is for WordPress/Mobile app developers who want to use Cincopa Easy Albums Plugin in conjunction with JSON API plugin as media gallery for their mobile app.
Features include:
<ul>
<li>Easy Albums Listing</li>
<li>Easy Albums Items Listing</li>
</ul>
The plugin was created to make available Cincopa Easy Albums Plugin Media listing for mobile apps via JSON API Plugin.
Hope this will help some.
For details, please check this: http://www.parorrey.com/solutions/json-api-cincopa/

JSON API Cincopa

Extends the JSON API Plugin to allow RESTful Cincopa Easy Albums Listing for any user

WPML to WP API vs JSON API Cincopa