Shy implies a timid reserve and a shrinking from familiarity or contact with others. There are 16 meanings listed in oed's entry for the word coy, eight of which are labelled obsolete (especially of women) being or pretending to be shy…
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Artfully or affectedly shy or reserved
See examples of coy used in a sentence.
If someone is being coy, they are unwilling to talk about something that they feel guilty or embarrassed about The hotel are understandably coy about the incident. Definition of coy adjective in oxford advanced learner's dictionary Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.
From middle english coy, from old french coi, earlier quei (“quiet, still”), from latin qu (i)ētus (“resting, at rest”) Doublet of quit, quiet, quite and quietus.