Airily is here: http://airily.jp/
But as far as I know they aren't really set up to support overseas orders. The order form only has support for Japanese addresses and nearly all payment methods are Japan-only (they do accept a few credit cards). In addition, tech support/staff contact is only available in Japanese ^^;
There is a bit of machine-translated English guidace here
but the bulk of the page is designed to cater to expatriates (ie. Japanese living abroad) and the assumption seems to be that those ordering from overseas will still speak Japanese as a primary language or will be able to get by on nothing but pictures. The site and order forms are Japanese-only. Navigating an order without Japanese ability is going to be tough.
International shipping for all orders is a flat 3,000 yen. That's over $35 ^^;;; It may still be cheaper to go through a middleman and have them SAL your purchase.
In any case: without Coscom and their discounts -- airily wigs are already in the $65-90 range after exchange. $35-40 shipping fees will pop each and every one over the $100 mark. It probably isn't the most practical choice for someone living abroad.
Sucks they won't be carrying them anymore
Zephyr has much better English support and will also ship overseas through rakuten:
If you're looking for wigs similar in quality and feel to the airilys but want to save $15 or $20 ~ http://www.rakuten.co.jp/vellsus/
is my favorite. They don't ship overseas, but they have frequent, very reasonable sales and a middleman should be able to give you a better base price on one than an airly (since they're cheaper to begin with).