The University of Cincinnati has an excellent website, https://drc.libraries.uc.edu/handle/2374.UC/2032 that includes info on births and deaths 1865-1912 for those persons that were born or died IN Cincinnati. .

Using your information, male, born 26 Dec 1904, mother born in KY, I found one possibility:

CONNER Douglas, MW (male white) born 12-26-1904, Home of the Friendless (which I presume is where the birth occured), father's name Jake REBEL, mother's name Mabel CONNER, father's birthplace blank, mother's birthplace Ky, father's occupation salesman, Dr. W. H. PRICE.

The Home for the Friendless and Foundlings is listed on page 1081 in the 1904 Cincinnati city directory as being at 433 W. Court. No further information but I believe the Home evolved into Maple Knoll. .

There is no Jake or Jacob REBEL listed in the 1904 or 1905 Cincinnati city directories.

You may want to check http://hcgsohio.org/cpage.php?pt=69 which includes some information on the above Home, including genealogical information.

I doubt that all births were recorded but maybe the above is your grandfather.

Good luck!

Bill