Hi Philip
I am not sure how helpful the following information will be but have found a Joseph and Mary of the correct ages in the 1860 USA census.
1860 census, Baltimore City, Maryland
Jos Stent, age 54, Carpenter, Value of personal estate 1000, born England
Mary, age 57, born England
Sarah Stent, age 36, England
Olivia, age 7, born Maryland
Kate Dinsmore, age 16, Dressmaker, born Ireland
This looks very promising, especially with the occupation albeit in Maryland, USA.....I have searched and cannot find anything else at all in any other census (used every possible search technique that I can think of...even the new wildcard search on Ancestry)
The only other thing for a Joseph Stent is a New York City petition for naturalization card dated 1839.
Details:
Joseph W Stent
Date of naturalization April 5th 1839
Address, New York City
Former Nationality, English
Witness to naturalization, Caleb Cridland, NY City
Those are the only details on the card and connect with the reference you have from the New York Genealogical Records. I have searched for Caleb Cridland who is on both the 1830 and 1840 census and looked at the images to see if Joseph was a neighbour (mistranscibed or mis -enumerated) but haven't found anything at all.
Sorry that I haven't come up with anything more meaningful but I will continue to search.
Best wishes
Yvonne