There is a widely circulating pedigree with few dates that shows Sion the son of "Old" George Swinney. I have not been able to find the evidence behind the widely circulating pedigree. The evidence that I have seen makes me think that Sion is the son of James and Catherine.
In 1820 in Lincoln County TN, James has 3 sons born between 1800 and 1810. In 1830, he only has one but there are two others in the County, Sion and Joseph. It makes sense that these are his other two sons. In 1840 Sion appears with a wife much younger than he has in 1830. In 1840 he has children that he does not have in 1850. In 1840 James and Catherine do not have children that they have in 1850. The children of the two households together (James and Sion) in 1840 fit the two together in 1850. In 1853 one of the young women in James and Catherine's household in Lincoln County TN in 1850 marries in Lauderdale County AL where Sion has moved. In 1856 another young woman from the 1850 Lincoln TN household of James and Catherine marries in Lauderdale AL and settles near Sion.
Yes, I think that Sion is James and Catherine's son. I think that after his first wife died he left most of his children from the first family with his parents in Lincoln County TN and moved with his new family to Lauderdale County AL. Then at least two daughters followed, married and settled near him. He is the right age to be James and Catherine's son. They were born in 1780 or before (depending on the Census) and as you say Sion was born about 1806.