Are you sure Adam & Daniel BURNER were in Licking Co, Ohio at that time? I checked the 1820 Licking Co, OH Census & the only BURNERs are Abraham, Henry, & John in Franklin Tp. I have also checked the following Licking Co, OH sources with no listing for Adam or Daniel.
1826 TAX INDEX - Lists Abraham, Henry, John
1816 TAX INDEX - Lists no BURNERs
1834 TAX INDEX - Lists Abraham, Henry, Henry Jr, Henry Sr
BRISTERS CENTENNIAL HISTORY OF NEWARK & LICKING CO, OH 1909 v.1 lists Henry, Henry Jr, J.V., Jacob (the following are listed under BURNET which I think may have been a typo=G.W., George W., J., James W., John, Rhoda); v.2 lists Catherine, Charles, Elizabeth, Etta F., George W., Hattie S., J.H., J.V., Katherine, Laura, Martha C., William, W.L.
PROBATE RECORDS 1828-1904 lists Abraham, Catherine, Henry, Henry Jr, J.V., Jacob V., Milton
CEMETERIES OF EDEN, FALLSBURY, & PERRY TPS (2 books) - no listings
MARRIAGES 1808-1875 lists Abraham, Catharine, Henry
COMMON PLEAS COURT RECORDS 1819-1822 - no listings
PARTITION RECORDS 1831-1836 - no listings
There are BURNETs, BENNERs (incl. a Daniel BENNER who gets married in 1819).
In BRISTERS v.2p.621 there is a sketch of a J.H. BURNER who came to Licking Co circa 1819, married Elizabeth CONDON in 1845, and had 7 children one of whom was a "D.E."....any relation?