No, the given pronunciation is correct. Kyra is a variant spelling of Cyra, feminine of Cyrus and Cyril, Kyrius and Kyril/Kiril(l), from the original Greek Kyrillos, derivative of the word kyrios meaning 'lord'. Some use it as a feminine of the Anglicised Kyran, from Ciara/Ciaran from the word ciar 'black' which is pronounced kee-uhr. So there's 'kie' like pie, 'kee' like see but not ever 'kai' like pay. The spellings Kyra and Kira are used interchangably in English because in English grammar y as a vowel takes on a long I sound. To achieve the pronunciation Kai-ra in correct English you would need to spell it either Kara and instruct as to a long A or Kaira, which illustrates your preferred pronunciation grammatically.
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