I have two Stoneham families in Ontario Canada. Joseph Stoneham (not sure of b-day) he married in Canada in May 1839, also on the old Census it states he's from England. (no specifics yet) Obviously not your Joseph, but you never know, could be a relation of sorts. The other family is John Stoneham (the 1851 Census has the last name spelt Stonom!)his father was Joseph also. they too were from England (no specifics yet) The area is Brampton Ontario, and Simcoe Co. Ontario.
Hopefully one of these days, I'll come across more detailed information on where in England they originated!