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

Chip Bennett

As of WordPress 4.3, this Plugin is no longer needed. The next update will integrate the Plugin into the core site icon feature, to allow for graceful 
retirement of the Plugin.
Add a Favicon to your site. No bells or whistles; simply upload a (ICO, PNG, or GIF) file.
Note: Plugin settings can be configured via Dashboard -> Settings -> Favicon.

cbnet Favicon

Add a Favicon to your site. No bells or whistles; simply upload a (ICO, PNG, or GIF) file.

Favicon Rotator vs cbnet Favicon