I've gotten you most of the way: JSFiddle.
The trick is simply to change the attribute of the img tag using jQuery's $.attr() method.
$('img').click(function() {
$(this).attr("onmouseover", "this.src='http://newevolutiondesigns.com/images/freebies/cat-wallpaper-7.jpg'");
})
You can easily write a function which checks the current value of this attribute, then sets the correct value on click. Hope this helps!