I didn't have any real luck...sorry. Have you tried the Licking County Genealogical Society (101 W Main St, Newark, OH 43055-5054, 740-349-5510)?
There were a lot of BARNESs in the area and many listings in the sources I have but I did not find Alexander or Anna Elizabeth (I did find an Anna E but the dates were later). I did find a Rachel BARNES marrying John D. DAVIS 23 Dec 1841 (Marriages 1808-1874).
There were DEANs, etc. but only a few DEALs: Marriages 1879-83 (Malissa, Rollin), "Licking Lantern" (George, Stephen).
The only MAGAWs I found were in: Probate 1828-1904 (James's estate 1858), Marriages 1874-79 (Jennie, Martha). There was a birth registered for Edith MAGAY (yes, Magay) born Eden Tp 6 Jul 1884, dau of Henry MAGAY & Jane J. DEAL. Another birth was registered for James McCoy MAGAW born Granville 9 May 1905, son of James E. MAGAW & Lulu SHINN. Obituary for William MAGAW 3 May 1900 at his son's home (Samuel), 95 years old. Obituary for Mrs. Jennie MAGAW, 88 years, d.18 Jan 1941 Mt. Vernon, OH, b.12 Jan 1853 Martinsburg, dau of Henry & Rhoda CARMICHAEL DEAL, children: Frank, Mrs. Edna LEONARD.