I'm assuming the whole first stanza is the correct answer: It little profits that an idle king, By this still hearth, among these barren crags,Match'd with an aged wife, I mete and doleUnequal laws unto a savage race, That hoard, and sleep, and feed, and know not me.
Duly means to do things in accordance in which is required or appropriate, so the opposite (antonym) would be improperly, which means doing things not in accordance or doing the opposing of accepted standards.
