Hello Janette,
I had another trawl through the films at Morpeth Library (Woodhorn opens 1st November), and I found the following:
Longbenton St. Bartholomew
Entry 1992 on 22 August 1841
William Gibbison, (parents) Joseph & Violet Tate, (abode) Long Benton, (occupation) hind.
Entry 2190 on 16 April 1843
Edward, Joseph & Violet Tate, Long Benton, hind.
Entry 279 on 14 March 1847
Joseph, Joseph & Violet Tate, Scrog House, hind.
The following sentence was written underneath but I had trouble deciphering a word; "According to the certificate of marinitted to me on the 15th day of March 1847".
Wallsend St. Peter
Entry 2197 on 13 April 1851
Oswald son of, Joseph & Violet Tate, Willington, labourer.
I would have expected to find your John Tate as well, but I noticed that the records for 1845 started in February 1845 (change of film), so it is possible that January 1845 was missed. I did not find any of their later children baptised at Longbenton or Wallsend. Earsdon was looked at again while I was hunting for my own relatives, but I saw no Tate family other than from a previous post.
Regards,
John