You don't need to extend the Page_Controller. Just put it in your SiteConfigCustom class

class SiteConfigCustom extends DataExtension {

public function getRandomImage() {
      return $this->BackgroundImages()->sort('RAND()')->First();
} 

}

and as far as i know, in your template file (Page.ss) you have to put the $ sign when using <% loop %>

<% loop $SiteConfig %>

<% end_loop %>

It may not work without the $.

If I put it up there, it breaks and I get the blank white page of death.

I don't believe the $ is necessary unless your doing something like <% if $MyDinner="kipper" %>

oh, made a silly mistake...it should be

public function getRandomImage() {
    return $this->owner->BackgroundImages()->sort('RAND()')->First();
} 

need the "owner" part when your in a DataExtension :). I think that might fix it.

That seems to work with this change to the template:

Page.ss

<% loop SiteConfig %> 
	$RandomImage.BackgroundImage
<% end_loop %> 

Thanks to all!

oh that's right. Good call on the template.

you could also use

<% loop SiteConfig.RandomImage %>
    $BackgroundImage
<% end_loop %>

if you wanted to loop through more then one random image.

Ok cool, thanks again!