From Longman Dictionary of Contemporary Englishbutton nose/eyesbutton nose/eyesHBHa nose or eyes that are small and round → button
Examples from the Corpus
button nose/eyes• There are hundreds of black button eyes and a thick nest of yarn for the hair.• Reddish brown hair and bright, button eyes, and a shy, quivering look.• Mrs Stych fixed her button eyes upon the elegant figure of Mrs Frizzell and bowled purposefully across the lawn. 