fishdan Jsonmaker lets administrators curate a nested tree of links directly on the front end. Drop the <code>[jsonmaker]</code> shortcode onto a page, expand nodes to add children, rename or remove items inline, and fetch any branch at <code>/json/<slug>.json</code>.
Highlights
<ul>
<li>Inline “Add”, “Edit”, and “Delete” controls for administrators (capability <code>jsonmaker_manage</code>).</li>
<li>Clean JSON endpoint for each node (<code>/json/<slug>.json</code>).</li>
<li>Store either URLs or plain text values; an empty value keeps a node as a container.</li>
<li>All data persists in a single WordPress option—no custom tables.</li>
</ul>

fishdan Jsonmaker

Manage hierarchical link collections via a shortcode, edit them inline, and expose any node as JSON.

David Shanske

Daniel Jalkut (Red Sweater)

mantonr

Adds a JSON Feed to your WordPress site by adding <code>/feed/json</code> to any URL.
The JSON Feed format is a pragmatic syndication format, like RSS and Atom, but with one big difference: it’s JSON instead of XML. Learn more at <a href="http://jsonfeed.org/" rel="nofollow ugc">jsonfeed.org</a>.

JSON Feed (jsonfeed.org)

This plugin is simple to install, adds no weight to your site, and does what it says on the tin.

fishdan Jsonmaker vs JSON Feed (jsonfeed.org)