Had this information ready to post last night and the computer ate it! Back to the drawing board....

Kentucky Marriages, Benton County:
Cecil Evans m. Leona Potters 1919, Volume 28, Page 115
William G. Evans to Margaret Crabtree 1881, Volume 5A, Page 272

1930 West Virginia, Mingo County, Chattaroy Township, ED#6, Page 47B, 4/18/1930:
Cecil Evans, 33yo, 1stM@22yo, KY KY KY, Miner/Coal Mine
Leona, wife, 28yo, 1stM@17yo, WV WV WV
Luther, son, 10yo, KY KY WV
Letha, daughter, 8yo, KY KY WV
Mary M., daughter, 6yo, KY KY WV
Junior B., son, 4yo, WV KY WV
Selicia?, daughter, 1yo, KY KY WV

Kentucky Death Index:
Green Evans 4/20/1925 Lawrence County, 62yo, Volume 60, Certificate #29953

1920 Kentucky, Lawrence County, Cherokee Township, ED#134, Page B, 1/3/1920:
Green Evans, 57yo, KY KY KY, Farmer
Margret, wife, 56yo, KY KY KY
John L., son, 19yo, KY KY KY, Farmer

Listed on same page....
Columbus Evans, 32yo, KY KY KY, Laborer
Rosey, wife, 31yo, KY KY KY
Willard, son, 11yo, KY KY KY

George Evans, 29yo, KY KY KY, Farmer
Lilley, wife, 25yo, KY KY KY

1910 Kentucky, Lawrence County, District 4, ED#100, Page 43A, 5/11,12/1910:
Greenville Evans, 48yo, M/30yrs, KY KY KY, Salesman, Dry Goods Store
Margarett, wife, 48yo, M/30yrs, 11 children/9 living,KY KY KY
George W., son, 20yo, KY KY KY, Farming, Farm Labor
Cecil, son, 15yo, KY KY KY, Laborer, Farm Labor
Cordelia, daughter, 12yo, KY KY KY
John L., son, 10yo, KY KY KY
Monroe, son, 7yo, KY KY KY

1900 Kentucky, Lawrence County, Twin Branch Township, ED#78, Page 184A, 6/1/1900:
Greenville Evans, 36yo, 11/1863, M/18yrs, KY KY KY, Farmer
Margret, wife, 34yo, 4/1861*, M/18yrs, 8 children/7 living, KY KY KY
Mary J., daughter, 16?yo, ?/1884?, KY KY KY
Columbus, son, 13yo, 10/1886, KY KY KY
George W., son, 10yo, 2/1889, KY KY KY
Liddia A., daughter, 7yo, 3/1893, KY KY KY
Cecil, son, 3yo, 2/1897, KY KY KY
Cordelia, daughter, 1yo, 12/1898, KY KY KY

1880 Kentucky, Lawrence County, Twin Branches Township, Voting District 11, ED#49, Page 346B, 6/26,28/1880:
G.W. Evans, 36yo, Farmer, KY KY KY
Sarah, wife, 33yo, Keeping House, KY KY KY
Wm. G., son, 16yo, Works on Farm, KY KY KY
Johnathan O., son, 12yo, Works on Farm, KY KY KY
James W., son, 8yo, KY KY KY
Amos D., son, 6yo, KY KY KY
Rhoda F., daughter, 2yo, KY KY KY

1870 Kentucky, Johnson County, Paintsville Precinct, Page 164B, 6/6/1870:
George Evans, 29yo, Farm Laborer, KY
Sarah J., 25yo, Keeping House, KY
Wm. Green, 6yo, KY
J.J. Critenden (Evans, male), 2yo, KY

Kentucky birth records for the 1938 time period should be kept at the state level and not in the actual county where the birth occurred. Try contacting the below noted:

Department for Health Services
Office of Vital Statistics
375 East Main Street
Frankfort, KY 40601