I cannot find a Harrison/Hull marriage either. I would agree that Stays is most likely Staithes - it is also known as Steers.
Is this Elizabeth Burnsides the Elizabeth
Burnside who was buried at St Cuthbert, Darlington on 26 May 1844, aged 64? If so, there is a brief article in the Newcastle Courant 7 June 1844 re: her death and the subsequent inquest. According to Elizabeth's daughter, the deceased was walking out close to her residence in Princess Square when she suddenly fell down and instantly expired. The verdict was "Died by the visitation of God." There is a death notice for Ambrose Burnsides in the Durham County Advertiser 24 June 1831 - at Darlington "yesterday se'nnight" aged 55. Burial St Cuthbert, Darlington as Burnside 18 June 1831.
There are other baptisms for children of Ambrose & Elizabeth. One on 28 Nov 1804 at St Andrew, Auckland is for Elizabeth, daughter of Ambrose Burnside, a n. of Blackwell, and his wife Elizabeth Watson, a n. of this parish. The plot thickens

ADDED: sorry, just found a marriage for Ambrose Burnside & Elizabeth Watson on 8 Oct 1803 at St Andrew, Auckland.