I have it working now, I had tried this code below before posting this question but I was missing the Post ID to assign it to so I just realized that and fixed it and it does work now!
Here is the code just in case it helps someone else in the future…
$photo_name="testimagename";
$newId = $post_id;
// Set Featured Image
$photo = new WP_Http();
$photo = $photo->request( $image_url );
$attachment = wp_upload_bits( $photo_name . '.jpg', null, $photo['body'], date("Y-m", strtotime( $photo['headers']['last-modified'] ) ) );
$filetype = wp_check_filetype( basename( $attachment['file'] ), null );
$postinfo = array(
'post_mime_type' => $filetype['type'],
'post_title' => $title . ' ',
'post_content' => '',
'post_status' => 'inherit',
);
$filename = $attachment['file'];
$attach_id = wp_insert_attachment( $postinfo, $filename, $newId );
if( !function_exists( 'wp_generate_attachment_data' ) )
require_once(ABSPATH . "wp-admin" . '/includes/image.php');
$attach_data = wp_generate_attachment_metadata( $attach_id, $filename );
wp_update_attachment_metadata( $attach_id, $attach_data );
set_post_thumbnail($post_id,$attach_id);