Hi,
Here is a possible marriage for David COLE,
David COLE
Jane CRIMBLE
Marriage: 08 APR 1833 Saint Marys, Portsea
This could be the eldest daughter Jane shown in the 1841 census,
Porchester Baptisms
Born 2 & Bapt 30 January1831
Jane
Illegitimate dr of Jane CRIMBLE
I've just checked the 1861 census and Jane is with her sister Ann CRIMBLE

RG9/649 f.94 p.25 Fareham
Gosport Rd
Jane COLE Head W 55 Housekeeper Porchester Hants
Anne " Daur U 27 Servant Hambledon "
Charles " Son U 23 Mariner " "
John " Son U 12 Scholar Fareham "
Anne CRIMBLE Sister U 61 Porchester "
Oh dear, I've just re-read your original post and you are looking for a David COLE born about 1813 Portsea, so the one above might not be yours. Where do you find David b.1813? It might help find him on the census.
Regards,
Daisy