Johann Koonce settled in NC around 1710. All in family killed in 1711 by Indians, except son George. He had sons Michael, Daniel and George, Jr. amoung others. All of these brothers named one of their children Daniel.
Michael Kooce was a Capt. in the NC Milita and served in the Rev. War also his wife Elizabeth (Eliza) was also recognized by the Gov. for her Rev. War Patriot Service for providing provisions.(Michael is How I got into the SAR). His son was named Daniel Simmons Koonce as that was the last name of Elizabeth, mother of Daniel.
Daniel Koonce (1734-1821), brother to Michael and George named his son Daniel, Jr.(1777-1860)
George Koonce,Jr. named one of his sons Daniel (d 1877).
I don't have much on any of the Daniel's children and I don't see an Elizabeth in any of them of the few I have. But a good guess would be Daniel, son of Michael and Elizabeth - you name your daughter after your mother. Suggest you check the US Census around your dates.