Here's a listing of such records, many of them have been microfilmed and are available at or through the Family History Library in Salt Lake City.
http://www.familysearch.org/

Whether any of these records are available online, I do not have that information. You might check with the USGenWeb site to see what it has available for Henry County.
http://www.usgenweb.org/

Good luck!

Georgia, Henry - Court records

Titles Corporation charters 1890-1926, Henry County, Georgia Georgia. Superior Court (Henry County)
County court minutes, 1880-1906 [Henry County, Georgia] Georgia. County Court (Henry County)

County officer, retail license, and druggist bonds, 1859-1889 (Henry County, Georgia) Georgia. Court of Ordinary (Henry County)

Court of Ordinary sitting for county purposes minutes 1888-1944, Henry County, Georgia Georgia. Court of Ordinary (Henry County)

Court records, 1926-1933 [Henry County, Georgia] Georgia. Juvenile Court (Henry County)

Genealogical resources in the Atlanta area Palgon, Gary M

Jurors' lists, 1888-1914 [Henry County, Georgia] Georgia. Superior Court (Henry County)

Lunacy records, 1897-1909 [Henry County, Georgia] Georgia. Court of Ordinary (Henry County)

Minutes and vouchers, 1826-1891 Georgia. Inferior Court (Henry County)

Minutes, 1825-1944 Georgia. Court of Ordinary (Henry County)

Minutes, 1866-1868 Georgia. County Court (Forsyth County)

Receipt records of tax collections, retail liquor licenses, estray sales, etc., 1850-1888 (Henry County, Georgia) Georgia. Court of Ordinary (Henry County)

Register of medical practitioners 1881-1957, Henry County, Georgia Georgia. Superior Court (Henry County)

Register of sales, 1829-1941 Georgia. Court of Ordinary (Henry County)

Superior Court bills, 1830-1890 [Henry County, Georgia] Georgia. Superior Court (Henry County)

Superior Court minutes, 1822-1906 Georgia. Superior Court (Henry County)

Superior Court writs, 1825-1909 Georgia. Superior Court (Henry County)
==============Myra