Coy belongs to the same old quiet word family.
Latin quietus meant quiet or at rest. Anglo-French quoi carried the word into English, where coy came to describe reserved behaviour.
Source
Merriam-Webster: coySelected historical forms, oldest first: Latin quietus → Anglo-French quoi → English coy. Each form is in the ancestry rather than merely a listed cognate. Selected glosses: quietus: Quiet or at rest; quoi: Quiet; coy: Shyly reserved.