Yi (and other characters) existed in Japanese a long time ago and I found an old katakana sheet that has the missing characters. This image is from 1873:
More on this at this Japanese wikipedia page for: ヤ行イ. Also, note that this page has the respective hiragana characters too.
In reality, most native Japanese will not be able to read the "classical yi" or other classical characters.
There are contexts where the classical characters are still used, most notably Yebisu Beer; look at the katakana character after 琥珀:
It looks like the katakana for "we"... which actually has me confused at the moment because I always thought it was "ye"...
Anyways! Although the beer is "Yebisu" in romaji and "Yebisu" (or "Webisu"?) in katakana, it is pronounced エビス.
To answer your question though you should probably go with イン as the others have suggested but if you really want to use the character for yi, it does it exist; just understand that most people will not be able to read it and, even if they can read it, they will still pronounce it イ.