On the 1851 census Hannibal and Christiana are in Thornaby Yorkshire with their children
Lovinah 14 born Yarm Yorkshire
Francis 11, Margaret 3 and Richard 11 months all born South Stockton Yorkshire.
Yarm parish registers I believe are on the IGI so it isn't likely they married there but perhaps it might help narrowing the search down to the surrounding area, in the absence of any other leads.
On the 1851 census Hannibal gives his birthplace as Acliffe Durham. On the 1861 census the family is in Guisborough Yorkshire. Hannibal gives his birthplace as Yackley Durham as does his brother Thomas aged 36.
Regards
Valda