Yes its the denomination that will crack the query, i looked 
Ros Davies Co Down website gives you 
Mr. . Hawkins . Donaghadee An Innkeeper; Death Notice 8 Oct 1795 NS
Mrs. Jane Hawkins . Donaghadee Widow Of John Hawkins; Mother Of John; Carrying On Business At Hillsborough Arms 25 Feb 1796 NS
Michael Hawkins . Donaghadee Of Carney Hill; Leased A House & 2 Acres In 1863 From Nicholas D. Crommelin GV  
Michael Hawkins . Donaghadee Husband Of Ellen Jane Mcclelland; Father Of Irvine Mckee Hawkins B. 16 Nov 1868 & Elizabeth B. 31 Jul 1871 CR
William Hawkins . Donaghadee of Shore St, Donaghadee; keeper of the public baths in 1846 POD
from familysearch.org an incomplete search found 
Jessie Hawkins Birth:  1814   Donaghadee, Down, Ireland Marriages: Spouse:  John Dick  
James  Hawkins Parents: 
  Father:  Michael Hawkins  Family 
Marriages: 
  Spouse:  Agnes Brown  Family 
  Marriage:  29 AUG 1856   Donaghadee, Down, Ireland 
  Wife Age at Marriage:  17
Donaghadee Church of Ireland just to the W of Main Street in Church Lane
Baptisms & burials from 1771 , marriages from 1772; graveyard attached; gravestone inscriptions available UHF Vol 16; email me for a gravestone look-up; also try 
http://www.bangor.homecall.co.uk/index.htmReferences;V7 p46, 47 OSM ; POD;NC; GIC; V16 MIs;GV; POD
1st Presbyterian Church
in the centre of Donaghadee town in High Street next to the Town Hall
Records from 1849; no graveyard 
http://www.presbyterianireland.org/congregations/donaghadee1.html http://www.emeraldancestors.com have a copy of the church booklet of 1925 with a church history on subscription 
References; V7 p 47 OSM ; GIPR: GIC ;GV; NC; POD  
2nd Presbyterian Church,
at the northern extremity of Donaghadee town in Warren Road/ Shore Street, on the sea shore
records from 1805; no graveyard; try 
http://shorestreet.org.uk/References; V7 p 46, 47 OSM: DR ; NI: GIPR; GIC; MIs;GV; POD  
Methodist Church
in Mount St., Donaghadee town across from Church of Ireland 
Graveyard separate; gravestones UHF Vol 17
 References; V7 p 47 OSM; POD; GIC; GV ; POD
using Griffiths layest website in 1863 griffiths.askaboutireland.ie/gv4/gv_
there is Hawkins  Michael  
Carney Hill   Down  Donaghadee   
Now back on family search are many more 
Carney Hill Hawkinseg Robert Francis Hawkins Pedigree 
Birth:  01 MAY 1880   
Carneyhill, , Down, Ireland 
Parents: 
  Father:  Michael Hawkins  Family 
  Mother:  Ellen Jane Hawkins McClelland 
so you may be able to knit them together, but which church were they going too.
Good luck, Jim