The most common writing of 'Ryuki' or 'Ryuuki' that I could find is the following:
竜騎
First kanji 竜: dragon
Second kanji 騎: to ride, rider
An alternative is 龍騎, but that also means "dragon rider".
I did not find it used as an actual name for a real person, but only as the name of the hero of an Anime TV series. See
http://www.animenewsnetwork.com/encyclopedia/anime.php?id=2168(Funny that the English translation of the name of this Anime is "masked rider", not "dragon rider".)