Hello Claud,
There is a note here
http://members.tripod.com/~Glosters/index-4.html about a private John Gardiner of the 61st dying in India during the mutiny on 4th July 1857. He could be your man?
You could try to see if he was on the medal roll for the Indian Mutiny - this would at least give you his army number. Then you could try for his service papers from the National Archives at Kew - this should give his wife's name and children, and show his parish of birth etc. But in the back of my mind I seem to recall that soldiers who died in service had their papers destroyed. But I may be wrong, and the experts on the Armed Forces forum on this site would know.
It may be possible also that his death, although in India, was registered in the usual way in England, though given the lag in communications in those days it may have been many months later or even in 1858. This cert, if available may yield further clues.
It was usual for widows of soldiers abroad in those days to marry again quite quickly, even within weeks, so you could also think of looking for a female Gardiner marrying in 57 or 58 on the overseas section of FindMyPast which may give you his wife's name. Again, a post on Rootschat for a look-up may help.