Archetyped

Favicon Rotator makes it easy to customize the favicon for your site. Just add a favicon via the administration page and it will be displayed whenever someone visits your site.
<h4>Highlights</h4>
<ul>
<li>New: Set icon for Touch devices (Android, iPhone, iPad, iPod Touch, etc.)</li>
<li>Simply point and click to add a favicon to your site</li>
<li>Supports adding multiple icons, from which a randomly selected favicon will be displayed.</li>
<li>Automatic icon conversion for large images (smaller files and faster loading)</li>
</ul>
<h4>Usage</h4>
<ol>
<li>Go to Theme > Favicon admin page to add/upload image(s) to use for the favicon</li>
</ol>
That’s it! The favicon will be displayed in visitors’ browsers when they visit your site
Notes
<ul>
<li>Verify that your theme uses the <code>wp_head()</code> template tag</li>
<li>If you add multiple icons, then a randomly selected icon will be displayed each time the site is loaded</li>
</ul>
<a href="http://archetyped.com/tools/favicon-rotator/" rel="nofollow ugc">More Information on Favicon Rotator’s Official Page</a>

Favicon Rotator

Easily set site favicon and even rotate through multiple icons

Web Guy

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Add a favicon.
Set the favicon URL under Appearance > Customize > Site Identity > Site Favicon.
This plugin is especially useful if you’d like to set a Site Icon, but also need to set a unique favicon separate from it.

Favicon Rotator vs Site Favicon