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The most common writing of 'Ryuki' or 'Ryuuki' that I could find is the following:

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竜騎

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First kanji 竜: dragon
Second kanji 騎: to ride, rider

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An alternative is 龍騎, but that also means "dragon rider".

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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".)