I checked the following sources for COVERs (I assume the name was never COVERT or COVERLY as I did not include these names):
Samuel COVER paid tax on land in Bowling Green Tp 1834 TAX LIST INDEX FOR LICKING CO, OH
John C. COVER, deceased. Joseph C., Mary Ellen, & John F., heirs. Mary COVER, guardian. Mary COVER & Solomon MIRES, bondsmen. 19 Apr 1855 LICKING CO, OH PROBATE RECORDS 1828-1904 p108
In Franklin Tp, Moundbuilders constructed mounds in the area north of Amsterdam. John COVER removed the two stone mounds "many years ago" and found skeletons in one of them. BRISTERS CENTENNIAL HISTORY OF NEWARK & LICKING CO, OH v.1p314 Sarah A. COVER married George W. MACK in Pennsylvania. She was a native of PA. Sarah died in 1906 in Brownsville, Licking Co, OH. Ch: Mary (wife of Henry BOOHER) & two sons M.C. (b.22 Aug 1871) & J.L. Ibid v2p748
Nothing in... PIONEER LIFE IN LICKING COUNTY 1816 TAX LIST INDEX 1826 TAX LIST INDEX 1834 TAX LIST INDEX 1820 CENSUS CEMETERIES OF EDEN, FALLSBURY, & PERRY TPS WASHINGTON CO, OH MARRIAGES 1791-1803 LICKING CO COMMON PLEAS COURT RECORDS 1819-1822 LICKING CO PARTITION RECORDS 1831-1836 INDEX OF LICKING CO PRE-1808 TRANSCRIBED LAND RECORDS LICKING CO MARRIAGES 1808-1875
These are the only sources I have at home. What sources have you checked? Have you tried the Licking Co Genealogical Society?