Thanks for that, Aghadowey!
MorrowCoulterClan,
I couldn't find anything on Morrows or Coulters in the Newtownards Methodist records but, as I now know they were Presbyterian, that's not surprising. Since everyone else seems to have pursued the other options I would have suggested (eg Emerald Ancestors, NIFHS, UHF, familysearch) I'm afraid I don't know where else you could look. Morrow's a fairly common name round here which doesn't help.
Sebrofa,
Sorry, can't find anything in N'Ards Methodist records that definitely ties in with the details you've given. The only White/Whyte records were the following:
Marriage 3rd January 1868
Samuel Smith, 27, Bachelor, Brickmaker, New Row, Donaghadee son of Samuel Smith, Mason
Isabella White, 27, Spinster, Back Street, Donaghadee, daughter of Alexander White, Sailor
Witnesses John Monk and Agnes White
Marriage 16th January 1885
Henry White, Full Age, Bachelor, Mill Worker, Movilla Street Newtownards, son of Alexander White (deceased) Labourer
Maggie Bennett, Full Age, Spinster, Mary Street Newtownards, daughter of Matthew Bennett (I think the occupation is Carman)
Witnesses John Bennett and Agnes (I think the surname is Edgin)
Baptism 6th September 1896
Born 2nd July 1896
Agnes White, daughter of David and AnnaBella White, Mill Street, Comber
I thought I'd try and see if I could find out any more about David, Mary etc and I see what you mean. I couldn't find David's death or a David/Mary marriage in the right location and timeframe either. Sorry I couldn't be of more help.