From
www.freereg.org.uk Nicholas and Mary's childrens baptisms South Shields St Hilda
Elizabeth born 28 Oct 1808 bap 23 Nov 1808 parents Nicholas Gray, shipwright native of
Swalwell and Mary Coe native of Fellon (Felling) Shore Gateshead - 1st daughter
Jane bap 6 Nov 1811 parents Nicholas Gray shipwright, native of
Whickham and Mary Coe native of Gateshead, 2nd daughter
George bap 6 Jan 1813 parents Nicholas Gray shipwright and Mary, living in South Shields
Grace bap 27 Oct 1816 parents Nicholas Gray shipwright and Mary, living in South Shields
So I would say from that Nicholas could have been baptised at Whickham (which covers Swalwell) and Mary in Gateshead, from
http://familysearch.org there is this baptism for Nicholas but it's a bit earlier than 1780
Nicholas bap 15 Dec 1772 parents Robert Grey & Grace, Whickham - although the mother's name could possibly be a clue
Nothing on familysearch in Gateshead for Mary although there is a baptism in Ryton Oct 1774 father William. Bit early again though.
Whickham, Gateshead and Ryton have Bishops Transcripts on familysearch so they would be a good starting point to check these 2 baptisms (and later ones) and see what clues there are - if any.
https://familysearch.org/search/image/index#uri=https%3A%2F%2Ffamilysearch.org%2Frecords%2Fwaypoint%2FMMRX-TTK%3A1643144822%3Fcc%3D1309819Shirl