How to improve my PHP adding script?
With regard to your question about adding ,, just do

$new_user_id = $_COOKIE['user_id'];

if ($subs['subscribed_user_id'] === '') {
  $new_user_id = $subs['subscribed_user_id'] . ',' . $new_user_id;
}


With that said, the details of how you add the comma is not the issue here.

I began rewriting the code, but since the db interactions make the code hard to test and work with, I honestly couldn't be bothered to properly finish it.

You should 


Wrap the functionality in a actual function taking parameters to remove use of $_ globals.
Stop using the ancient and deprecated mysql extension. In fact, don't use (the much better) mysqli either, at the very least, adopt PDO, or better yet, a tool that removes the low level details of managing the DB.
Fix the injection vulnerability in your update query.
Consider whether you really should be comma separating values in the column. Perhaps you should instead add a new row?


Some code I started writing, but didn't finish because I have better things to do than setting up the db I would need.

function update_user_id($user_id, $subs, $cookie) {
  $subs = mysql_fetch_array(mysql_query("SELECT subscribed_user_id FROM users WHERE user_id = " . (int) $user_id));

  $subs_array = explode(',', $subs['subscribed_user_id']);

  if (!in_array($cookie['user_id'], $subs_array)) {
    $new_user_id = $cookie['user_id'];

    if ($subs['subscribed_user_id'] === '') {
      $new_user_id = $subs['subscribed_user_id'] . ',' . $new_user_id;
    }

    mysql_query("UPDATE users SET subers = subers + 1, subscribed_user_id = '" . $new_user_id . "' WHERE user_id = ". (int) $user_id);
  }
}