Mostly appears as a modifier for related words:
育婴师 (yùyīngshī, 'certified baby-care professional'),
育婴堂 (yùyīngtáng, 'foundling home / orphanage' — historical),
育婴假 ('parental leave'). Rarely used as a standalone verb in casual speech, where
带孩子 (dài háizi) or
照顾婴儿 is more natural.