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Synonyms for Round-eyed (same or very similar meaning)

WordNet sense 1 (exhibiting childlike simplicity and credulity):
childlike, simple, wide-eyed, dewy-eyed

WordNet sense 2 (marked by or showing unaffected simplicity and lack of guile or worldly experience):
naif, naive

WordNet sense 3 (having large round wide-open eyes):
saucer-eyed

WordNet sense 4 (having an eye or eyes or eyelike feature especially as specified; often used in combination):
eyed


From the ODE community, based on WordNetadd/edit