If I remember correctly the japanese IME from the Japanese Magic set is floating about.
Do a search for iWnnIME. (Note: no font replacement necessary, the Droid Fallback font has Japanese inside)
(this seems to work on my unit, don't know about you...)
Note that this does NOT fix a bug that's been around since 1.6 that affects your music player. The Android Media Scanner software doesn't handle non-English characters correctly, and hasn't done so for, um, ever.
Move "sig". For great justice.
Galaxy S2 i9100 OmniRom Nightly 0106 / Dorimanx 10.43v60 beta
Galaxy Camera EK-110 (stock rooted) (It only ever came with 4.1.2 so.)
Ouya (stock rooted) (it only ever came with 4.1.2 so.)
Liquid Community ROM 1.4 (Acer Liquid)
O2 XDA Atom WM6.1 Kuruma Final
HTC Touch Elf Opal Ultimate 3.2.1
LG KS20 Kiss20.4