During a brief pause in your wailing, gnashing of teeth, and general lamenting, you wistfully Google some more only to find that the missing volumes are available online, in English, for free on any of a number of manga aggregation websites. Through the diligent and unpaid efforts of a legion of amateur scanners and translators, you can enjoy the further adventures of all your favorite characters! But no sooner have you started to enjoy this cornucopia than you discover the awful truth: manga aggregation sites are EVIL, having caused a major collapse in the market for legally translated manga, leading to the demise of many publishers, and doing nothing to recompense the artists who originally created the work or the publishers who originally issued it in Japan. (See Cecilia d'Anastasio's fascinating article "The Invisible Labor Economy Behind Pirated Japanese Comics.")
So you find yourself on the horns of a dilemma: you can't use manga aggregation sites, because they are EVIL, but you have to, because your pathetic fan life depends on it! How to deal with this mire of cognitive and moral discord, not to mention the probability of enduring many many rebirths in dark Buddhist hells (or whatever brand of inferno you happen to subscribe to)?
The answer, at least for now, comes from a post in the "Learn Japanese" Reddit called "Buying Japanese Kindle Ebooks from amazon.jp." Yes, there is a way to salve your conscience. Go ahead and read the manga at an aggregation site. But buy a Japanese copy of the book to support the original authors and publishers! And, to avoid killing trees for a copy that you can't read anyway, buy the Kindle e-book version.
Alas, navigating the Amazon.co.jp website is not an easy task for an English-only speaker. The Reddit post mentioned previously has a few tips, but it can still take quite a lot of futzing around for an American to get Kindle orders working properly on Amazon.co.jp. The following steps are provided here to save you the trouble (and perhaps to save your very soul!):
1. Open a web browser and go to https://www.amazon.co.jp/. Once there, right-click the JP globe below the search bar and choose Translate to English.
2. Create a new account. To do this, click the down arrow next to Account & List, then click Are you new to the registration?
3. On the Create Account screen, enter your name in both the Name and Phonetic boxes. Reportedly, you can enter the same E-mail address that you use for your Amazon account in the U.S. However, in that case, you must be sure to specify a different Password. I actually used a different E-mail address than my U.S. account, so cannot promise that using the same E-mail address will actually work.
4. Click Account & List to go to the Your Account screen, then click 1-Click Settings.
5. Click Add an International Address. On the Add a New Address screen, fill in your information and then click Save & Add Payment Method.
6. Click Enter information on the new payment method. Fill in information for your credit card. (Important: From my experience, you need to use a credit card and not a debit/credit card, as debit/credit cards do not seem to work for overseas purchases.) Then select your billing address. You are returned to the Manage default address and 1-Click setting screen, and the message "The update has been successfully applied" should appear.
7. Under 1-Click status, click turn on. At this point, you are now able to complete purchases from Amazon.co.jp, but some more steps are needed to enable you to purchase Kindle books.
8. From Account & Lists, choose Your Content and Devices. On the resulting screen, click Settings, then click Country Settings. Next to Current country, click Change.
9. On this screen we're going to indicate that you live in Japan. This is a requirement in order to be able to purchase Japanese Kindle e-books. On the Country of residence screen, enter your Full Name. For the ZIP/Postal Code, put a three-digit number in the first field and a four-digit number in the second field. (I used 123 4567.) You can leave the Prefecture as Hokkaido. Fill in random information in Address Line 1 and Address Line 2. Leave Company Name blank. Fill in your Phone Number. Click Update.
10. Back on the Manage Your Content and Devices screen, on the Settings tab, under Kindle Payment Setting, click Edit Payment Method.
11. On the Kindle Payment Setting screen, choose the credit card that you defined earlier, then click Done editing.
You are now able to order Japanese Kindle books. However, locating the books you want to order may take some research. You might find what you want by entering the author's name in English letters, or the English language title. More likely you will have to poke around on the Internet until you find the author's name in Japanese or the series title in Japanese. One place to look is in Wikipedia; if they have an article on the author or the book series, the article typically includes the spellings in Japanese characters. Once you have the Japanese spelling, you can enter it in the search box in Amazon.co.jp.
Here are listings for the first volumes for some of my favorite series:
Good luck! Let me know if you have corrections to these instructions.
After using the above method successfully for some time, I recently encountered an error on Amazon.co.uk where it said that I couldn't order any more Kindle books while traveling out of the country. I found that others have run into a similar problem. I found a solution in the thread Legally purchasing Japanese Kindle books / audiobooks. Before opening the browser and navigating to Amazon, you need to launch a VPN that connects to the Internet through a server in Japan. One free VPN client that has worked for me is VPN Gate, which is available at http://www.vpngate.net/en/.
Elsewhere I have seen a recommendation that you can buy Japanese ebooks through eBookJapan, a firm that does not care what country you are located in. For details, see the article How to Read Japanese Manga Online (A Guide to Building Your Manga Library with eBookJapan). Unfortunately, though I was able to follow most of the steps in the article, I wasn't able to actually complete an order. An error occurs whenever I try to complete a purchase using a credit card. I hope you have better luck if you attempt to use this method.