Does Joomla have a method or object that I can use to get the DELETE request parameters from? I am not seeing it anywhere. This is for Joomla 3.0
I am not sure if this request types are working. Check this out:
$jinput = JFactory::getApplication()->input;
echo "Method is: " . $jinput->getMethod();
$x = $jinput->get('x');
var_dump($x);
I'm not sure about DELETE, but for PUT check this out: PHP: PUT method support.
There's Joomla Web Services Working Group that recently published Joomla CMS Web Service API Implementation.
Although Web Service API is not part of current Joomla distribution yet, this is recommended way to design your REST API.