earlier records would include church records etc and the irish genealogy hub has indexs of Co antrim Tithe Applotment Book entries 1823-1837, which sometimes helps going further back in time but it is incomplete
http://www.irishgenealogyhub.com/antrim/tithe-applotments/larne-parish.php has no
Harbeson, Harbinson, Harbison, Harbusson, Herbertsan, Herbinson, Herbison
however there is an entry for a Mullen variant
Mullin, Thomas Townland: Ballylorran Year: 1834
I can supply all the entries for Co Antrim but without a knowledge of civil parishes you might need help there is a free map with numbered list iof parish names
Coal mining in Co Antrim existed see the book by Alan McCutcheon industrial Archaeology of Northern Ireland