Nothing definite but there are clues that may help with further research.
Nathaniels' Rev War pension application says he has two children he's supporting -- "George Niles" and "William Anson Niles."He doesn't say they are "his" sons and he mixes up who had the middle name Anson. Their names wereactually George Anson Niles and William Niles. And in his pension application he understates their ages by several years, perhaps to enhance his chances of getting the pension.
Geo A Niles and Wm Niles lived in the Brooklyn CT area with Wm eventually moving to IN where he died in 1856 at La Porte IN. (He married Roxana Russell in CT at Brooklyn.)Geo married a Dolly __ and both were alive in 1880 at Killingly, Windham Co.,CT. He gives his father's birthplace as CT and mother's as RI.
The name of Wm's parents from LDS records are said to be Ephraim and Esther (Cornell) Niles who married 14 Oct 1792 at Providence RI.So, it's possible the 1880 census for Wm is accurate when he says his mother was born at RI. Both Wm and Geo A. Niles were born in Ga from census data.
There was an Ephraim Niles at Savannah, Chatham Co., Ga., according to tax and newspaper records. (The GA US Federal censuses for 1790, 1800, and 1810 are missing.) He lived in Savannah on Carpenters Row and had a business there with John Cole. Ephraim is mentioned in the local newspapers from about 1793 to mid 1805. A daughter name Lydia died on 20 Aug 1805, age 18 months of teething. Another man "Luther Green, age 40, died at Mr. Niles's near the Fort, left a wife & 4 children at Newport, Rhode Is."
One of Wm's children was named Esther (later a physician), born 1831 CT, possibly for his mother. Could Ephraim have been the brother of Nathaniel Sweet Niles of Pomfret, CT? Nathl may have cared for Wm and Geo after their parents decease.It seems unlikely Nathl had two sons born in Ga, named Geo and Wm.
One of Nathaniel's children born 11 Jul 1799 was named Lydia. It may just be a coincidence that Ephraim's daughter, born in 1804 and died the next year, had the same given name.
Who were Nath's and Ephraim's parents? A wild guess might be Benjamin 5 (David 4)and Ruth Niles of W. Greenwich RI. Ruth was the dau of Nathaniel 5 and Ruth (Sweet) Niles.Possibly Benjamin and Ruth (Niles)Niles may have named a son Nathaniel Sweet Niles for her parents.
The W. Greenwich towns records for 26 Feb 1776 lists a "Nathl son of Benj" on the Militia 3rd Company roster. I've not found another RI source to confirm that he actually served in RI. He may have and then gone to CT to serve in Aug of the same year. It's not clear he was born in RI or CT nor what he was doing in 1776 in W.G., RI.
Benjamin and Ruth Niles were both deceased by 1784 according to her father's will made 25 Mar 1784. Where Benj and Ruth lived after they married and died isn't yet known. They had at least one child: George Niles whose birth was recorded 29 Mar 1750 at West Greenwich, RI.This Geo lived at W.G, RI, and Freetown MA (where his father was from),later at Danbury NH, and last at Fairfield, VT, where he died in 1821 intestate. He was literate, a Constable, town selectman, and Capt of Militia. He was literate whereas Nathaniel Sweet Niles was not; not unusual for one brother to be literate and another not. Possibly Benj and Ruth had other children, maybe born in CT.
Another possibility is that the middle name Sweet could be for a friend of his father's. There were Sweets in the Pomfret area. The records of the known four children of Nathl should be searched to see if there is any proof of where their parents were born.