Not sure if you already have all of this but the baptismal parish register entry of Josiah COLE snr is available to view on Ancestry. He is baptised on 12 May 1816 but shown as born on 12 July 1796, son of John & Susannah COLE, Chatteris, Labourer. All three of his marriage records are also available to view on Ancestry, i.e. his marriage in 1816 to Mary HUDSON, then on 24 April 1857 to Sarah GOODMAN, widow, father Elisha SKINNER and finally on 30 July 1867 to Hannah CLARKE, widow, father Richard PECK.
A possible parish register burial record at Chatteris for Mary COLE on 8 December 1852, aged 55, given that they are both alive in the 1851 census. The children of Josiah & Mary are shown in the parish register as Martha on 10 April 1817, John on 11 October 1818 and William on 1 October 1820. No other baptisms to Josiah & Mary are shown in the parish register nor in my Cambs FHS Baptismal Index which goes up to 1837 which is interesting given that the 1851 census shows another two children for Josiah & Mary both being born in Chatteris. Nor am I having much luck finding Josiah jnr after the 1851 census record
Janet