I've been tasked with implementing a rōmaji keyboard in a medical device. As I understand the problem, the user is to be permitted to enter katakana, hiragana, and/or kanji via the rōmaji keyboard. I have resources covering the mapping of rōmaji to katakana/hiragana symbols; however, I'm having difficulty locating resources to guide mapping of the resultant katakana to kanji symbols. Can anyone recommend a resource that would assist in mapping the katakana to kanji?
Mostly it's just obtaining a list of kana -> kanji conversions that will solve your problem. You can find that in any freely-available dictionary database, such as EDICT. Creating your own is going to be difficult on the same order of magnitude as writing a dictionary.
However, what really determines the quality of an input method editor (IME) for Japanese is how well-sorted the results are, e.g. when I type きょう, the first result should be relevant to the other things I'm typing. There is, unfortunately, not an easy solution to this problem, and mostly I imagine it will require a lot of resources (time or effort) to reach a satisfying solution.