How to render a user register form for a Profile2 type
After looking through the Profile2 Git repository viewer for v1.3. I believe you want to do something like the following using profile2_attach_form. The `profile2_attach_form has the following API comment and function signature:

 /**
 * Attaches the profile forms of the profiles set in
 * $form_state['profiles'].
 *
 * Modules may alter the profile2 entity form regardless to which form it is
 * attached by making use of hook_form_profile2_form_alter().
 *
 * @param $form
 *   The form to which to attach the profile2 form. For each profile the form
 *   is added to @code $form['profile_' . $profile-&gt;type] @endcode. This helper
 *   also adds in a validation and a submit handler caring for the attached
 *   profile forms.
 *
 * @see hook_form_profile2_form_alter()
 * @see profile2_form_validate_handler()
 * @see profile2_form_submit_handler()
 */
function profile2_attach_form(&amp;$form, &amp;$form_state) { /* ... */ }


So, you could use it as follows by slightly modifying your code:

$user_register_form = drupal_get_form('user_register_form');
$form_state['profiles'] = array(
    'CUSTOM_PROFILE_TYPE_NAME' =&gt; profile2_get_types('CUSTOM_PROFILE_TYPE_NAME')
);
profile2_attach_form($user_register_form, $form_state);
print(drupal_render($user_register_form));


If you need to tweak any profile entity form displayed in some of your registration page(s), you may want to implement the specific FORM_ID version of hook_form alter, hook_form_profile2_form_alter().

EDIT 01/15/2015

minor API clarification and code cleanup from comments.