Maybe even a way of celebrating childbirth is to change bit by bit. I can not guess how many people younger then me would follow what I think as of a traditional Japanese style.
[[Cash]]
I would choose cash if I offer a gift on childbirth to my friend who is so familiar that I can look after or name her baby. A baby might be given baby items by the parents, their relatives and their neighbors. Even if they don't need that, it's not easy to throw away a gift from a close friend. Money does not cause this kind of problem.
Speaking of customs, I suppose usually we send cash for congratulation in one, three or five 1000-yen or 10000-yen banknotes; we don't make it in an even number, especially never in four on childbirth. There is no need I presume to get fresh bills ready for a friend, but ones without folds are preferable. If you hope to use an envelope, I recommend asking your acquaintance in Japan to purchase one which is already made only for childbirth. (As to envelopes for monetary gift we have various types of design, some are for condolence.)
[[Telegram]]
Can you know the place of childbirth? If so, then how about sending a telegram? I have never sent one from overseas. Maybe a telecommunication company you know has a route between you in the U.S. and your friend in Japan.
At least two Japanese companies handle international telegrams to be sent to Japan. (I couldn't find English editions of the two websites). They both offer mounts of orthodox design as well as pretty decorative ones. In a case your acquaintance can send the telegram within Japan, you can choose NTT East / NTT West, but please don't forget to say it's from you in your message.
I suppose it's OK if your telegram reaches her by the time of "oshichiya" (literally "the seventh night") celebration on the seventh day from the date of birth.
-- KDDI Evolva
: List of fares (in JP yen) with links to mounts (explained in Japanese)
http://www.denpoppo.com/ryokin.htmlYou can attach your handwritten message you've saved in a picture file of JPG, GIF or PNG format.
-- Nippon Denpo Service
: mounts for congratulation (explained in Japanese)
http://www.nippondenpo.com/order/board_arts/index/1/1: examples of messages (explained in Japanese)
http://www.nippondenpo.com/www/rei4.htmMessage #1902 is in English (It costs 29 US dollars for 46 - 49 alphabets). You can make use your own message typed.