Try going through the marriages of Troia both groom and brides name for Liguori and see who the parents are you are looking for father Gaetano Liguori mother Grazia Viola Troia marriage indexes I have a few the marriage indexes are about 350-400 pages apart PG LINK https://familysearch.org/pal:/MM9.3.1/T ... ,349047201 Year Page 1872-481 1873 812 1874-1115 1875-1394 1876-1671
After looking at Michelantonio Liguori death record he was 54 when he died 1887 in Troia making him born about 1833 so you will have to order films of Registri dello stato civile di Troia (Foggia), 1809-1929 to continue your research for he records online start at 1866 PG LINK TO FILMS OF TROIA 1809-1929 https://familysearch.org/search/catalog ... %20Library
From the marriage allegati heres the 1845 Oct 11th in the town of Troia birth record of Luigi Liguori son of Carmelo Liguori age 33 (abt 1812 son of deceased Luigi Liguori) and his wife Maria Rosa Albani age 25 (abt 1820 daughter of Giovanni Albani) PG LINK TO RECORDS https://familysearch.org/pal:/MM9.3.1/T ... ,349052401
Supporting documents [processetti or allegati]. These documents were often filed by the bride and groom in support of their intent or "solemn promise" to marry. Records proving their births and their parents’ births and deaths and sometimes documentation on earlier generations may be included. The names of former spouses and their death dates are also provided.