Beginning in 1853, a law required that births & deaths be reported in the county of residence. However, it seems that most were not. In 1917, the West Virginia Department of Health Vital Registration began collecting the county reports of births & deaths and issued certificates.
The West Virginia State Archives has the BIRTH records ONLINE:
THE FOLLOWING RECORDS WILL REMAIN ON THIS SITE AS A QUICK REFERENCE.
Copied from LDS Family History Film, #0163911.
There are NO records in this film for the years 1863, 1864, 1870.