Edit in JSFiddle

d1 = document.getElementById("d1");
b1 = document.getElementById("b1");

var done = new Event('done');

d1.addEventListener('done', function(){d1.innerHTML = Math.random()});

b1.addEventListener("click", 
                    function(){
                        //b1.innerHTML = Math.random();
                        b1.dispatchEvent(done);
                    });
b1.addEventListener('done', function(){
   d1.dispatchEvent(done);
});
var radioButton = document.createElement('input');
radioButton.setAttribute('type','radio');
var text = document.createTextNode("testing daddy");
document.body.appendChild(radioButton);
radioButton.addEventListener('click', function(){
document.body.appendChild(text);}, false);

var radioButton2 = document.createElement('input');
radioButton2.setAttribute('type', 'radio');
var text2 = document.createTextNode("second test");
document.body.appendChild(radioButton2);
radioButton.addEventListener('onclick', function(){document.body.appendChild(text2);}, false);

<div id="d1"></div> 
<button id="b1">button</button>
<p>"click" works but only for the first click with a radio button</p>
<p> "onclick" does not work. </p>