There are no marriages recorded in the Belford Presbyterian registers, as Michael explained it was only legal to marry in the Church of England.
If George & Eleanor married in the area of Chatton/Belford, you ought to check Belford Parish registers first. You have checked Bamburgh so I think you should also check Lowick, Wooler, Kyloe and Doddington as outside chances, maybe even Holy Island and Chillingham.
If they went to Scotland and married in a Presbyterian church there, try Mordington and Coldstream registers.
However, I am afraid the most likely probability is that they married irregularly at Lamberton Toll or Coldstream Bridge or any of the other places where marriages took place on the border, in which case your chances of finding a record is minimal!
You have now found out what a minefield you have wandered into here!
Happy hunting,
Jora