In my opinion, you should do the best you can within the time constraints to write her a supplementary letter, making as strong a case you can while still being honest. Here are a few points informing this opinion:
There's nothing ethically wrong with giving the obvious impression that you think one student is better than another, while supporting both.
Having said that, if you give one student an "extra" letter and not the other, it could be interpreted as a signal that you specifically don't think the weaker student deserves to be selected.
You already suggested that she ask someone else, and she hasn't, which probably means you're her best option.
Alternatively, you could try to find the email address of someone involved with this application process, explain the entire situation to them, and ask for guidance.