It is important to note that the character Tsuruya in the anime Suzumiya Haruhi no Yuuutsu never actually says nyoro~n. She does say nyoro, which is a meaningless speech quirk (much like ending every sentence with desu or nyo).
Nyoro~n is solely the catchphrase of Churuya and is a portmanteau of Tsuruya's catchphrase, nyoro, and the Japanese onomatopoeia for disappointment, shobon. Churuya (and her many spinoffs) typically says it when she has become the victim of misfortune.
