My James Coulter came to the US about 1840 [per census] and was married to a Julia. That's all I know about him. In 1863 his son Patrick [born about 1830 in Ireland enlisted in the Union army on Sept 4, 1863 at Cairo, Illinois.

After his discharge in Alabama in April 1866, Patrick showed up in PA in 1866, then married Elizabeth Wert in 1867 in Tremont, Schuylkill Co, PA. They apparently stayed there until Aug 23, 1871 when their son James was born. Sometime after that they moved on to Shamokin Co. [Coal Twnshp in 1880 census] when son John Coulter [my ggpa] was born on Jan. 19, 1875. Between June 1884 and Jan 1887 they moved to Gloucester City, NJ [across river from Philly] when son William was born.

I have no info about siblings of James or Patrick. It's doubtful that Charles [not possible to have been born anytime else in 1871] could have been a twin of James because church records list James' baptism, Charles is not with the family in 1880 census, the 1900 census in NJ shows number of surviving children [all accounted for], and a 1904 CW pension document does not list him among the named surviving children.

What I can't rule out is that Charles could be a son of Patrick's brother. I have not found the immigration papers for James and Patrick nor an 1850 or 60 census record for them.

I hope this helps you in some way even if it's only ruling out Patrick as his father.