"Prying" could be translated curiosus ("inquisitive") or perhaps percuriosus ("very inquisitive"). "Prying eyes" would then be oculi [per]curiosi. Remember that in Latin, the form of the words varies depending on how they're used; oculi curiosi is the form taken by the subject of a sentence, or the thing spoken to ("O prying eyes!"). Other forms are:

oculos curiosos: object of the verb

oculorum curiosorum: "of prying eyes"

oculis curiosis: "by, with, to or for prying eyes"