Sydney spent the earliest years of her childhood at the Owensons' home at 60 Dame Street in Dublin with her mother Jane and sister Olivia. Sydney was primarily educated by her mother, but she also received tutoring from a young boy named Thomas Dermody, a local prodigy whom their father had rescued from poverty. Her mother died in 1789 when Sydney was about ten years old, and her father sent her and her sister away to private schools to finish their education. Sydney spent three years at a Huguenot academy at Clontarf and then attended a finishing school in Earl Street, Dublin. After completing school Sydney moved with her father to Sligo.