elemind

Plugin will allow you to fetch the WP REST API call with a “lang” variable. 
It will retrieve the right content from WPML.
Tested with the latest version of:
<ul>
<li>WPML 3.2.7</li>
<li>WP REST API 2.0-beta4</li>
</ul>

WP REST API multilanguage (over WMPL)

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

WP REST API multilanguage (over WMPL) vs JSON API Cincopa