It is very "likely" that Johnathan P. Crow's parents, based on the 1900 census record of Johnathan P. Crow's parents birthplaces, both SC, that his parents were John William Crow who married Avis Porter in Franklin Co., GA on 20 October 1831.
John William Crow was born between 1810-1813 in SC, and was living in 1850, Dwelling 862, pg. 61, Division 88, Walton Co. GA, close to Newton Co. GA, where Johnathan P. Crow married Miss Allbritton in 1865.
In the household of John William Crow in 1850 was a Jonathan P. Crow, age 8, (c1842) born in GA.The age is off a bit, but I believe this is your Johnathan P. Crow (1845-1904).
One way to support this theory would be to find a living male Crow(e) from one of Johnathan P. Crow's sons to do a DNA test, if there are any living.