I found quite a few places that do ear piercing, but it was not easy to find a place that would do baby's ears.
Here is a place I found in Azabu Juban. It is a proper skin care clinic and has good reviews. I spoke with the receptionist today and she assured me that babies are ok.
Primo Azabu Juban Clinic
You'll need to ask a friend who speaks Japanese to make the appointment and who can translate at your appoitment.
Please keep in mind that if you are planning on sending your daughter to a non-international school in Japan, ear piercing is typically not allowed until university.