Accidentally deleted an input method

Okay, I created an account on this forum specifically for this, since I find my problem pretty frustrating. I recently started grooming my newly bought mac with some tools like monolingual and onyx. I had set it up in a way (both in mac OS and in monolingual) so I could switch easily between Belgian input, U.S. and Japanese (Kotoeri). However, when I did a seemingly basic maintenance function with Onyx, my Japanese input function disappeared, leaving me unable to type in Japanese characters. Of course, I have already roamed the internet, looking for a solution, but none have been working until now. In fact, the only one I've seen involved using the install disc, but since I'm using a retina, I don't have a disc bay or installation disc whatsoever. I can't believe there's not an option of simply re-downloading the input method, also, I can't even find it back in the back-ups I made some hours before (or maybe I'm looking in the wrong folder).

I would definitely appreciate anyone's help.
Cheers,
David

Oddly, I still have Japanese listed under my languages. However, it's not listed under input sources anymore, this is the one I actually need.

Still nobody that can help me out? I've been looking all over the web for this but haven't found a single answer. I would assume it would be as easy as looking for the language input files on another mac but I can't even find them anywhere.

Alright, for those experiencing the same problems: I now just downloaded google's Japanese IME application. After installment it also appears in your input method list, and quick switching using ctr-space is possible. It's a little bit different but apart from that it works fine. いいですね
If anyone else finds a way to retrieve the actual Apple input method, let me know!