Patrick Kennedy

My gg grandfather, Patrick  Kennedy, was born in Killybegs, Co. Donegal in 1840, per his civil war pension record. He was married to Mary Jane Smith and had 7 children. His son Anthony is my g grandfather. He lived in Cook county Illinois and died 1916/17. Allegedly immigrated in 1860/61. Grave location is known. Confirmation of birth info and parents is unknown.  Any help would be appreciated.