I've checked my Jeff. Co. Birth Records Books but his birth wasn't listed. I believe registration wasn't required by law until 1916. I checked Delayed Birth Records and he wasn't listed there either.
I know his WW1 Draft Registion shows he was born in Jefferson Co., Ill.
Have you tried obtaining his marriage certificate to see if parents are listed or his death certificate and obit.?
Do you know the names of any of his sibblings? I believe his parents might have been Joseph I. and Lucy Ann Carter?? I've found two marriages in my books with parents names for both of Joseph's two marriages.
I believe his widow (second marriage) is shown in the 1900 census along with several children but John Carter Gray is not listed with the family. I have info. on this family if you need it.
I have a ton of Jefferson Co. genealogy books and would be happy to go thru them if you can give me any other leads or info. or if you want me to search for other lines.