Finding a birth certificate can be difficult because of various privacy laws.
You should be able to check the Birth Index and also check the SS applications records on ancestry. another sources is the Kentucky School Census
Kentucky had a yearly school census that listed the head of Household, all school age children and their dates of birth. These started in mid 1880's and continued to the mid 1930's. These are not extant for all counties. Pike County, does have most of them and they are available at the Kentucky Dept. of Libraries and Archives (KDLA). They will research the information for you for a fee if you can't research for your self.
I believe the Kentucky Historical Society also has the microfilms. I would suggest checking their catalog.
Some counties still have them at the County Clerks office or have turned them over to the school boards.
I would suggest checking for more than one year to check for continuity in the names.