Hi,
Do you know the names of Frank's children?
He is not listed in the 1901 or 1911 census as living in Cork. The only Peppers listed in Cork in 1911 are Bertram Laurence Pepper and his wife Ethel Theresa both born in England. Might Bertram be Frank's brother? and he joined them in Cork.
http://www.census.nationalarchives.ie/reels/nai001889192/ I did come across a birth of a Henry Sidney Pepper in Fermoy Co. Cork on 13th December 1894 giving his father as Frank and his mother Marianne nee Gunstore ( looks like it???) Frank's occupation is soldier and his address at that time Old Barracks Fermoy.
https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1895/02225/1839155.pdfThere are only two Frank Peppers in 1911 census and have ruled out both as one only 17 and the other aged 30 and a soldier in Belfast but listed as single.
As other responders have said St. Michaels (Church of Ireland ) cemetery Blackrock is the most obvious it would be a good idea to contact them and they would certainly be very willing to look up the burial records for you. There is another St. Michael's cemetery (RC) in Blackrock but it only opened in 1960's.
Some other options for possible burial place are
Templehill cemetery, Ballintemple, very near to Blackrock - No records available for this cemetery.
St. Josephs, Tory Top Road
St. Finbarrs Cathedral, Cork City ( C of I)
St. Finbarrs cemetery, Glasheen Road, ( multi denominational).
I checked out a book by well known Cork historian Richard Henchion titled East to Mahon,
The story of Blackrock, Ballintemple, Ballinlough, Ballinure and Mahon ( all adjoining areas).
Lots of information on burials at Templehill and some on St. Michaels C of I Blackrock but no mention of Peppers or Almaville.
Another suggestion re burial if a poster has a subscription to old newspaper records they might be willing to do a look up of the death notices at the relevant time and sometimes it might mention the cemetery. You could also contact the Cork County library - local studies department and they are very helpful and would probably look up the newspaper death notices for you.
https://www.corkcoco.ie/library-services/local-studies-family-historySorry we can't pinpoint the exact burial place for you.
Mary
Celtic Liberty