Not sure who the owners were in the period you are looking at but the Annesley estate records are held at the Public records office in Belfast
Annesley family, Viscounts Glerawly and Earls Annesley: deeds, estate, family and legal papers, 17th-20th cents [Public Record Office of Northern Ireland, D1503, D1854]; estate maps, 1813-92 [Public Record Office of Northern Ireland, T2452]