I think some people have had luck with amazon Japan. You have to create a different account and you have to add a Japanese address though. You can look up a hotel in japan and use that, although you have to type (or paste) Japanese. After all that, your US credit card might work. I haven't tried this method, only heard that it works for some people. My method is different but requires a Japanese 3DS.
That's the way I do it. The Japanese 3ds has until now always accepted my card. Last time I tried was last week when I added funds in preparation for MHXX. I'm sorry it doesn't work for you :-( maybe Nintendo changed something and next time maybe it won't work for me..... check with your credit card company though. Sometimes they might flag international transactions. If it was the card company, you should be able to sort it out with them. If it was Nintendo Japan themselves who denied the transaction, then you might be out of luck :-(