I stumbled across this solution to add attributes to the read more links of a node.
/**
* Implements template_preprocess_links()
*/
function MYTHEME_preprocess_links(&$variables) {
$variables['links']['node-readmore']['link']['#options']['attributes']['class'][] = 'button';
$variables['links']['comment-add']['link']['#options']['attributes']['class'][] = 'button';
}
Thanks: http://drupal.stackexchange.com/a/186323