If you can't find birth info at the local level, be sure to check the county and state levels. Don't overlook this valuable resource. Be sure to examine various churches' records in the area you are researching. Just because your family is a particular religion today, doesn't mean that a family member didn't attend a different church at some time. Pay close attention to Godparents and witnesses, as they could be family members too.
Doctors notes on deliveries at home seem to be few and far between.
Our local archives only has two records of Doctors' actual notes of the deliveries made. Be sure to check the Genealogy Societies, and Historical Societies for possible records. Don't overlook the possibility of a Midwife being present at the birth of an ancestor. Be sure to check the local libraries and societies for info. More recent records are confidential, but you might get lucky and find some older records if you dig deep enough.