name:    James Brewster
registration district:    Ballymoney
event type:    DEATHS
registration quarter and year:    Oct - Dec 1897
estimated birth year:    1809
age (at death):    88
volume number:    1
page number:    88
digital folder number:    4200681

This, I assume, is NOT him:
Date of Death :26 July 1897
Surname :Brewster
Date of Grant :23 December 1897
Forename :James
Reseal Date :
Registry :Belfast
Effects :Effects £29 10s.
No Image
Full Abstract :
Administration of the estate of James
Brewster late of Dunseverick County Antrim Fisherman who died 26 July 1897 granted at Belfast to Mary Brewster of Dunseverick Spinster the Daughter.

Name: Rachel Brewster 
Registration District: Coleraine 
Event Type: DEATHS 
Registration Quarter and Year: Jul - Sep 1884 
Estimated Birth Year: 1810 
Age (at Death): 74 
Mother's Maiden Name:
Film Number: 101592 
Volume Number: 1 
Page Number: 274 
Digital Folder Number: 4200674 
Image Number: 00447 

Source: David Brewster's' brother's tree on A.com

This is the only John Brewster who fits the bill in Civil Records (of Deaths) - someone born near to the age of James in the 1840s and died after James went to Landhead (he was there for the 1901 Census) and before the 1901 Census in Ballintaggart:
name:    John Brewster
registration district:    Coleraine
event type:    DEATHS
registration quarter and year:    Apr - Jun 1889
estimated birth year:    1854
age (at death):    35
volume number:    1
page number:    343
digital folder number:    4200677