Here is a list of places I buy manga online. All places deal with manga in Japanese.
eBook Japan: Obviously, this place sells e-books. And they let you use non-Japanese credit cards. You can also subscribe to magazines so you will purchase them automatically when they are released. You have to download their app to read the books. You will accumulate points and you can use them towards future purchases. UPDATE: As of March 2019, you had to relocate to the Yahoo service which now does not let you download the app from overseas. People are angry because eBookJapan was supposed to be a service which people living overseas could use. We are still waiting for an update from Yahoo, who says it’s highly unlikely that they will make it available for overseas customers.
Kinokuniya: I’ve never ordered from them before, but apparently they have a new e-book service that works for those living overseas. It’s worth trying out now that eBookJapan doesn’t work for overseas customers.
Rakuten Books: You can buy ebooks from Rakuten (via non-Japanese credit cards) and read them in your Kobo reader app available worldwide.
Honto: This place sells both e-books and actual books, but the app is only available from Japanese accounts. They often give out coupons or have sales for e-books so you can get great deals. You have to download their apps to read books. You can use non-Japanese credit cards and they will mail around the world. They have the SAL shipping option. You can accumulate points here as well.
Horin Love Books: This place specializes in Boy’s Love books mostly. They will also ship around the world and you can ask for the SAL option. This place gives out extras with some books. You can use non-Japanese credit cards. Note: as of November 2018, they only ship with the EMS method.
ComiComi Studio: This place also gives out specials with various books and specializes in Boy’s Love books as well. They ship around the world but only have the expensive EMS option. You can buy using non-Japanese credit cards.
Mandarake: You can buy used books here. You sometimes have to search often if you are looking for something rare. Prices are sometimes expensive for popular rare items. They mail overseas and you can use non-Japanese credit cards. Website is in English but for best results search in Japanese fonts.