Not knowing the area well, I found info about the places you mention. Current Google maps show Kilbegs road running into Milltown road about1 mile nw of Antrim town. Could her address Dunsilly be Dún Cille Bige (see Downkillybegs (Dún Cille Bige) Drummaul. Could his address Milltown, in Killybegs Drummaul , but now might be located in Antrim civil parish.
Around 1834 neither last name is listed in the Tithe Applotment Books for Drummaul civil parish see
http://www.irishgenealogyhub.com/antrim/tithe-applotments/drummaul-parish.php#Around 1833 neither last name is listed in the Tithe Applotment Books for Antrim civil parish see
http://www.irishgenealogyhub.com/antrim/tithe-applotments/drummaul-parish.php#You mention baptisms at Randalstown the downloadable quide to PRONI church records gives the lists as below., but you will need to look it up to copy their micro film or fiche holdings wjich they also list together with if any records are in local custody{ie the church itself etc} PRONI also has the same sort of information for Antrim civil parish.
DRUMMAUL, CO. ANTRIM
C.I. Drummaul (Connor diocese)
Baptisms, 1823-1989; marriages, 1823-46 and 1862- 1992; burials, 1823-1900; vestry minutes, 1851-70.
Vestry minutes, 1851-; preachers’ books, 1891-.
M. Randalstown
Baptisms, 1829-1987; circuit schedule books, 1860- 94; membership register, 1826-91.
P. Old Randalstown
Baptisms, 1853-1944; marriages, 1845-1922; marriage notices, 1962-2001.
P. 1st Randalstown
Marriages, 1845-1934; marriage notices, 1869-2001.
P. 2nd Randalstown
Baptisms, 1850-1986; marriages, 1845-1936; marriage notice books, 1869-1998; session minutes, 1850-95.
R.C. Drummaul (Randalstown) (Down and Connor diocese) [Includes the civil parishes of Drummaul and Cranfield and up to 1873 the parish of Antrim]
Baptisms, 1825-81; marriages, 1825-84; deaths, 1837- 48.
I cant help further, good luck onwards