Hi
The three birth certificates (one of which you already have) will pin point further the movement of the family in England before and after the 1841 census, Albert's confirming the 1841 census 
Births Mar 1838  Stephenson  Leonard Quintus    Sunderland  24 201 
Births Dec 1840   Stephenson  Albert Peak    Scarbro  24 475 
Births Dec 1843 STEPHENSON  Alfred Septimus     Gateshead  24 15[35] 
If John was still alive at the time of Alfred's birth, then since the birth was registered in Gateshead and the family were still in Gateshead in 1851 the first place to look for his death would be in Gateshead.
There are 4 possible death registrations
Deaths Dec 1844  
STEPHENSON  John    Gateshead  24 95    
STEPHENSON  John     Gateshead  24 97    
Deaths Jun 1845 STEPHENSON  John     Gateshead  24 100    
Deaths Dec 1846 Stephenson  John     Gateshead  24 138 
It is possible to see the civil registration subdistricts of Gateshead these deaths were registered in
http://online.gateshead.gov.uk/bmd/John STEPHENSON Died: Q4 1844 Register: 3 HEW Entry:257
John STEPHENSON Died: Q4 1844 Register: 3 HEW Entry:273
John STEPHENSON Died: Q2 1845 Register: 3 WIN Entry:115
John STEPHENSON Died: Q4 1846 Register: 4 HEW Entry:130
I think HEW is Heworth sub district and WIN is Winlaton
This search engine doesn't find Alfred's birth.
The 1851 census puts the family in the ecclesiastical district of St Marys.
The 1845 death appears to be a John Stephenson aged 2 burial in Gateshead
In 1846 there is a burial of a John Stephenson in Heworth aged 1
http://search.labs.familysearch.org/recordsearch/start.html?datestamp=1204024901500#startThere are no records on this source for the 1844 deaths. Neither of the 1844 deaths may of course be correct. It is just that I can't eliminate them.
Two further baptisms for the family - baptised with Leonard whose baptism was already given.
Harriet Elizabeth Mariana Stephenson born 4th October 1833 
Christening:  21 SEP 1838   Bishopwearmouth, Durham
Father:  John Stephenson  
Mother:  Elizabeth Stephenson  
Katharine Mary Layton Stephenson  born 21st July 1835
Birth:  Christening:  21 SEP 1838   Bishopwearmouth, Durham
Father:  John Stephenson  
Mother:  Elizabeth Stephenson     
LEONARD QUINTIES STEPHENSON 
Christening:  21 SEP 1838 
Birth:  16 MAR 1838   Bishopwearmouth, Durham
Father:  JOHN STEPHENSON  
Mother:  ELIZ.  
The baptisms can be found on Family Search
http://www.familysearch.org/Eng/Search/frameset_search.asp?PAGE=igi/search_IGI.asp&clear_form=trueand also on Family Search Record Search where addtional information is given
http://search.labs.familysearch.org/recordsearch/start.html?datestamp=1204024901500#startsuch as Henry Layton Stephensons baptism date 1st April 1833 Singhee Bengal
Where is Story's Buildings? It might be where they were living in 1838 but it is given on one of the baptisms in the index as John's birthplace - information which would be extremely rarely given on children's baptisms so it is unlikely to be correctly indexed
A further baptism which will be of interest because of the middle name
John Bromswell STEPHENSON
Baptism Date: 01 April 1833 
Location: Ghazeepore
Parents: John; Elizabeth
Notes: Born at sea
http://indiafamily.bl.uk/UI/Home.aspxFrom the Family Search Record website but from a totally different Presidency - Madras not Bengal so may be not connected. Presumably the diary would state whether they were in that area
16th January 1831 
William Samuel Stephenson
John and Elizabeth
St Thomas Mount Madras
27th September 1834 born 20th July 1834
Mary Elizabeth Stephenson
John and Elizabeth
St Thomas Mount Madras
Regards
Valda