What can I do?
Nothing. You will not get a reservation at Jiro's, forget it. You need to be extremely well-connected, rich or lucky (better yet, a combination thereof) to land one, even as a local.
If you are well connected, ask your connection to ask for you. If you are rich, stay at a very expensive hotel, and ask them to ask for you (if you have a credit card with a concierge service, that could also work). If you are feeling lucky, ask your Japanese relative to call the number on the homepage and pray that the call gets through, and if it does get through, pray again that they will talk to you.
Update (November 2019): Sukiyabashi Jiro has been kicked out of the Michelin guide because the guide considers that it "does not accept reservations from the general public".