This transcription record found on FindMyPast has his date of death as 2nd March 1900:
First name(s) J
Last name Cunningham
Year 1899-1902
Rank Private
Service number 3544
Regiment 1 Battalion The Devonshire Regiment
Memorials Cathedral. N Transept. Tablets County, Exeter, Devon, England
Event unit 1 Battalion The Devonshire Regiment
Event detail Died Disease on 02/03/1900 at Ladysmith
Event source Natal Field Force. JB Hayward & Sons
Notes QSA Clasps: E,DoL
Country Great Britain
Record set Anglo-Boer War Records 1899-1902
Category Military, armed forces & conflict
Subcategory Boer Wars
Collections from Great Britain, UK None
Following up on the record cited by Sturgy:
The marriage of an Ellen Cunningham to a Daniel O'Shea was registered in Q2 1880 in Middlesbrough.
I have found said Daniel & Ellen on 4 (messy and not totally agreeing) Public Family Tree on Ancestry. 3 give the date of marriage as 26 June 1880. They all agree Ellen was born in 1862 but only one supplies the only available Census Return for Ellen before she married i.e. the 1871 one. This shows both her parents were Irish, her mother was called Jane but her father's name is illegible to me. Their children are: William 20, Jane 12, Ellen 10, Elizabeth 7 and illegible again 4. The Ancestry transcriber has the illegibles as Geol but has deciphered the badly written (but obvious to me) Cunningham as Connaghan. I think Geol is an Irish name meaning born at Christmas. Excluding James (Geol) himself this is a perfect fit for the record cited by Sturgy. Perhaps James did not like his Irish name and adopted James.
Looking for a Geol Cunningham born c1867 in Middlesbrough on the 1881 & 1891 Censuses got me nowhere. A couple of possibilities arose using James but it was obvious they both lived until 1911.
David.