I've been doing some scouting around the internet [even though these people are not related to me!] and here is a line which I think is the most likely candidate for George W. Costley's ancestry:
The 1860 census of Kane Precinct, Greene Co. IL on p 885 lists WILLIAM COSTLY, 59 wm, farmer, b KY with wife ELIZABETH 59, and kids Andrew 31, Madison 22, GEORGE 18, Maria 15, Caroline 13, Louisa 10, Sarah 7, Evin 9.They are the only Costly/Costley family in Greene County.
I had found reference to George W. Costley being born in Greene County, IL on an Ancestral File entry for Curtis Clayton Conard, which gave me the Costley surname for his wife Fannie from whom he was later divorced.
There is a nice little bio sketch of "Maj. William Costley" in the History of Greene and Jersey Counties, Illinois (1885) by Wm. McAdams, page 786, which says that William was born 15 Oct 1801 in Kentucky, but was reared mostly in Missouri.His parents were William and Margarette.The family came to Greene Co. in 1819 and the father died shortly thereafter.Around 1823, William [the son] married Elizabeth Mathis and had 15 kids [unnamed in the article].He had the first public house between Carrollton and Alton.Gained his title from service in the militia.He died at home in Kane Pct. 31 Jan 1869.
I found George Costley, 26, and his wife Elizabeth, 25 and kids Frank 5, Andrew 4, and Clara, 1 on the 1870 census of Montgomery County, IL, page 283, and next family was Morgan [Madison?] 34, his wife Melvina 28 and some kids.
Another Ancestral File entry gives the surname of Margarette Costley [Maj. William's mother] as HUNTER, the daughter of George Washington HUNTER and Angeline MOORE.
Hopefully this will give you some clues toward further research.Good luck in your hunt.It looks as if George Costley might have named his daughter Clara after a sister [see 1870 census info above].
If you wish, you can contact me directly by email and we can work a little more on this together.