In a quick check of what I have at home I didn't find much.
*1830 Census Index for Ohio: 0 Tirey, Tyre, Tyree, Tarry, Terro, 31 Terry 0 in Licking Co.
*1840 Census Index for Ohio: 0 Tirey, Terro, Tarry, 2 Tyre (Doyd Tyre p73 Clark Co & William Tyre p100 Scioto Co), 1 Tyree (p299 Whitfrel Tyree Cincinnati 7th Ward Hamilton Co), 51 Terry 0 in Licking Co.
*1850 Census Index for Ohio: 0 Tirey, Tyree, Terro, 6 Tyre (Emery, James, & John all on p60 Licking Co), 2 Tarry (Franklin p214 Cuyahoga Co, John p312 Medina Co), 233 Terry
(These indexes include the federal census & 'special' census, & some mortality schedules so actual numbers may be less).
*Early Licking Co Home Register Index 1838-72 lists a Mary Tire.
*Licking Co Cemeteries & Surname Index lists Tyre buried in Grove Cemetery, Licking Tp, & Terry buried in Wilson Cemetery, Newton Tp, & Mt Sterling Cemetery, Hopewell Tp, Muskingum Co.
*1834 Tax Index lists a William TERREY owning land in Eden Tp & a Margaret Tarrey owning personal property in Eden Tp.
-There were a few listings of Tyrer & Tirer. Also checked, Bristers Centennial History v1-2, Chancery Index 1819-24, Pre1808 Land Records, Washington Co Marriages 1791-1803, 1809, 1810, 1816, 1826 Tax Indexes, Marriages 1808-1888, Newark Directory 1858/9 (Rosa Tirer servt Church & 3d), Hills History did list Tyrer, & Probate Records 1828-1904,
I'll take your query with me the next time I visit the Licking Co Genealogical Society.