Might have him. On his marriage his father is listed as William
There is a birth registered for a Joseph Davis Dec qtr 1876 Aston (matches dob 1939), mmn Hartland.
There is a marriage registered for a William Davis to a Rosina Mary Hartland listed Jun qtr 1871 Lambeth.
On 1881 census there is a Joseph Davis living at Gibb St, Aston with grandparents Henry and Rebecca. Henry is a bricklayer born Worcestershire. Also there is Nelly aged 3, which matches a Nellie Davis registered Aston Mar qtr 1878, mmn Hartland.
On 1851 census a Henry Davis (bricklayer) is living in Tewkesbury with wife Rebecca and children, including a William b1838 Tewkesbury.
On 1901 census William Davis born Tewkesbury is living in Brighton with wife Rosina and a daughter Winifred. Winifred is 19 and born Brighton and there is a birth registration listed for a Winifred Zella Davis Mar qtr 1882 Brighton.
With Joseph's 2 daughters named Winifred Zella and Rosina Mary seems too much of a coincidence for it not to be him.