The name Raynes is registered in counties Down, Mayo and Kildare start of 1900.
No hits for the name in Cork
Saying that Henry C Raynes was Harbourmaster and might have worked in Cork for a period of time and moved back to where they came from.
Had a look in the 1911 census and found 7 records in the whole of Ireland for the name Raynes
The name Ryalll gives 128 records, found no Henry C but DID find a John George Ryall born about 1858 and his wife Susannah and son Thomas Robert, all born in Cork. John George Ryall was a J.P Farmer I do not know what that means. 2 children were born son Thomas only survived, he was born about 1885. They lived in house number 3 in Ballynoe (Gortroe, County Cork)
The Ryalls were members of the Church of Ireland, giving away the English background a bit.
The first Ryall in Cork was John Ryall born about 1842 in County Cork, who lived with his son Thomas born 1866 in county Cork and his sons wife Mary born 1871 in county Limerick.
The eldest Raynes was Martin Raynes born 1838 in County Galway, farm servant of the Grady family of Slievemahanagh, County Mayo
So a good bit of information on the Ryalls but hardly anyting for the Raynes name.
Hope you can use this information, happy searching
Annemarie