If the Japanese Wikipedia page is to be believed, the kanji would be the following:
Yosuga: 縁
Shijima: 静寂
Musubi: 結
These make a decent bit of sense to me, although I'd probably go with 黙 for Shijima, myself. It has the same meaning as the compound given above, can be read the same way, and isn't a compound. Probably worth noting that all of these kanji, including the two-character compound for Shijima, have other, much, much more common readings, so it's entirely probable that unless the person reading them is a reasonably well-educated Japanese speaker and a huge Nocturne fan, they'll assign them different readings. But yeah, if you're looking for kanji for the Kotowari, those should be the ones you want. Also, just in case you need the kanji for Kotowari, it's 理.