By default there is no Japanese input in Samsung keyboard. I know there is a plugin called Multiling with it's HanWriting plugin but it only supports 1 letter by time. Is there a way to handwrite Japanese in sentence ?
I use the Simeji input method. it uses the great "flick" method for inputting kana. It takes some getting used to, but is very fast once you do. To switch between keyboards, just long press in the text field.
I don't think there is a handwriting app, at the moment. At least, not for writing, although there are some for practicing Kana and Kanji.
For typing, I currently use Google Japanese Input (10 MB, Free), it's reliable and seems solid to me.
You have two choices: one is typing the Romaji, the other one is typing Kana directly. In this second way, you click the 行 (gyou). For example, click on the Sa-gyou to choose the syllables that start with s- (sa, shi, su, se, so), then swype towards the one you want.
A visual example in the image below: the user chose the Ra-gyou (ra, ri, ru, re, ro), and swyped towards "ri", highlighted just above.