Inputting Japanese characters? I am not a Japanese speaker, but I know a few words, mostly Pokémon names... In fact, in many cases the Japanese name will pop up in my head before the English one.

But I want to be able to type アブソル instead of "Abusoru" because the Romaji makes it look silly.

However at present the only way I can do this on my phone is to find an online converter and copy the result from there. Hardly ideal. But I can't find Japanese input methods anywhere in the keyboard settings. Plenty of other writing systems like Greek, Arabic, and I think Chinese, but no Japanese. Am I simply overlooking an option, or is there something I need to do to get such support on my phone?
Please take a look at Google Japanese Input: https://play.google.com/store/apps/details?id=com.google.android.inputmethod.japanese

Swype keyboard has Japanese language built in as well: https://play.google.com/store/apps/details?id=com.nuance.swype.dtc