Delaney was born in 1871 in Fernandina Beach, Florida to Daniel Sharp Delany, who worked as a pilot on a revenue cutter called the George S. Boutwell, and Anna M. Delany. She was Henry Beard Delany's niece and goddaughter, and her middle name came from his. Her family name varied in spelling, versions included Delany and De Lany. Delaney joined the Baptist church at the age of thirteen.
