I have done this in the JavaScript:

function myFunction() {
  head = document.getElementsByTagName('head');
  links = head[0].getElementsByTagName('link');
  for (var i in links) {
     link = links[i];
     if (link.getAttribute('rel') == 'shortcut icon') {
        link.setAttribute('href', '/userContent/favicon.ico');
        break;
     }
  }
};
var body = document.getElementsByTagName('body');
if (window.addEventListener) {
  window.addEventListener('load', myFunction, false);
}
else if (window.attachEvent) {
  window.attachEvent('onload', myFunction );
}

How did you inject the JavaScript code into Jenkins? I really don't to end-up with GreaseMonkey -like client plugins.

Having the same icon on all Jenkins instances is insane from the UX point of view.

This was a while back, but what I recall and have reconstructed is this:

• Using the SimpleTheme plugin, this config file org.codefirst.SimpleThemeDecorator.xml:
  {{<org.codefirst.SimpleThemeDecorator plugin="simple-theme-plugin@0.3">
  <cssUrl>/userContent/nucleator.css</cssUrl>
  <jsUrl>/userContent/decorate.js</jsUrl>
  </org.codefirst.SimpleThemeDecorator>
  }}

Then, in the Jenkins installation directory:
mkdir userContent
put the above XML file in the install dir.
put the Javascript from the earlier comment in userContent/decorate.js
and I have a css file that looks something like this:
{{

#header .logo {
height: 80px;
}

.logo {
background-image: url("my_logo.png");
display: block;
width: 406px;
background-size: 406px 80px;
margin: 5px 0px 5px 10px;
}

.logo img

HTH.

Custom plugin for this: https://github.com/buzztaiki/jenkins-favicon-plugin

Fixed with release 0.4