Userscripts.org

The problem is: This feature is defined in the User Channel javascript, not in the watch page.
I think this feature is more suited to be in a dedicated script.

Here a start:

// ==UserScript==
// @name           Youtube Add Friend Button
// @namespace      http://userscripts.org
// @description    Youtube Add Friend Button
// @include        http://www.youtube.com/*
// ==/UserScript==


(function() {

//***************************************************
var innerscript = function() {//Start of innerscript

  add_friend=function(name) {
    alert(name);
  }

}//******************************//End of innerscript
//***************************************************

function AddInnerScript(script) {
  var scriptElem=document.createElement('script');
  scriptElem.setAttribute('type','text/javascript');
  scriptElem.textContent="("+script+")();";
  document.body.appendChild(scriptElem);
}

function Add_Script() {
  AddInnerScript(innerscript.toString());
}

function Add_Button() {
  var user=document.evaluate('//a[contains(@class,"contributor")]', document, null, XPathResult.FIRST_ORDERED_NODE_TYPE, null).singleNodeValue;
  if(!user) { return; }
  var username=user.textContent;
  var Elem=document.evaluate('//div[@id="subscribeDiv"]', document, null, XPathResult.FIRST_ORDERED_NODE_TYPE, null).singleNodeValue;
  if(!Elem) { return; }
  var DivElem=document.createElement('div');
  DivElem.setAttribute('style','text-align:right; margin-top:2px;');
  var linkElem=document.createElement('a');
  linkElem.setAttribute('class','yt-button yt-button-urgent');
  linkElem.setAttribute('href','#');
  linkElem.setAttribute('onclick',"add_friend('"+username+"'); return false;");
  spanElem=document.createElement('span');
  spanElem.textContent='Add Friend';
  linkElem.appendChild(spanElem);
  DivElem.appendChild(linkElem);
  Elem.parentNode.appendChild(DivElem);
}

Add_Script();
Add_Button();

})();