I am not a genealogist - but this is what I found.
The church is St. George's that you are referring to is The Ebenezer Methodist Church , 7 York Street, St. George's Bermuda, GE05 Reverand Greta Smith telephone 441-297-1771 or fax number 441-297-8057
The graveyard is also located in St. George's. It is on the waters edge and most of the head stones are worn.I cannot say for sure if the one you are looking for is there or not.
My own ancestors attended Ebernezer Methodist Church in St. George's and infact my own Great Grandparents were the second couple to write in the register - Henry John Wilson and Mary O. S. Gibson in 1877.
In 'The Bermuda Index L/Z' compiled by Hallett. (info taken from old newspapers). Page1278 to page 1282 under the surname STEWART. Years covered July 10, 1819 to April 24, 1913.
Entry dated March 9, 1859:- Your Rev. Charles Stewart, aged 38, a native of Edinburgh, minister of the United Presbyterian Church at Brisbane, Morton Bay, Australia, died on March 2 in St. George's, at the residence of his brother-in-law, A. Hall, Quartermaster, Cameronians.
19th Century Wills of Bermuda - compiled by Hallett Page 332 - surnames in Capitals.
STEWART, Charles, Rev. 1858, Feb. 11 - 1858, March 29 - W20:298 Late Minister of the Gospel, Brisbane, Moreton Bay, New South Wales, now res St. George's. Sister Elizabeth STEWART/HALL, wife of Archibald HALL (Q Master 26th Reg. Foot), Exec: sister Elizabeth, wit: Isaac SUCKLING, Samuel Salton SMITH, Geo MELDRUM.
I do not see a burial notice in the 19th Century Church Register of Bermuda - by Hallett for Rev. Charles Stewart which makes me wonder if maybe he was actually taken back to his home for burial and not buried here. There is nothing under St. George's burials. Nothing under Methodist burials, nothing under Presbyterian burials, nothing under Dockyard Ireland Island burials either (maritime).
19th Century Church Registers of Bermuda - by Hallett (this may or maynot be your ancestor) There is nothing found on Archibald Hall).
Hall, Elizabeth - 34y 9m - Pembroke Parish - burial, 1881 Sep. 13th - comment: On Agar’s Island, Bermuda; Of Kent, England.
I hope I have been of some help.I would suggest that you contact the Ebernezer Church, as they may be able to help you.
Two other books I looked at is Hallett's - Chronical of a Colonial Church and Hallett's - Forty Years of Convict Labour in Bermuda,there is nothing under the surname STEWART in either book.