Hi there,
I've done a search through my records and have pulled out all the Elizabeth marriages around that period:
ALNWICK 17 December 1769, Elizabeth Morton to William Henderson, both of this parish. Wit. John Shell, John Morton
GATESHEAD Elizabeth Morton and Thos. Massey, married 14th of April 1776
TYNEMOUTH Elizabeth Morton of this parish and Robert Chater of this parish, by Licence, married 25th of November 1780. Wit. William Linskill, John Chater [Durham Marriage Bonds Robert Chater, Tynemouth, 26, Labourer and Elz. Morton, Tynemouth, 32; bondsman John Reid, Tynemouth, parish clerk]
HORTON BY BLYTH Elizabeth Murton and Martin Greaner, by Banns, married 19 January 1782
CHATTON 29 April 1784, Elizabeth Murton of Chatton Bridge End in this P. and Thomas Thompson of Reaveley Greens in the P. of Ingeram, by Banns. Wit. John Morton, William Brown
ALNWICK 2 February 1789, Elizabeth Morton and George Stamp, both of this parish by banns. Wit. Thos. Dunn, Thos. Patterson
NEWCASTLE ST JOHN Elizabeth Murton and Edward Pattison, both of this chapelry, married 4 April, 1798
SOUTH SHIELDS, ST. HILDA Elizabeth Morton and Robert Richardson, married 24th of November 1800
SOUTH SHIELDS, ST. HILDA Elizabeth Murton and Joseph Hall, married 4 September, 1803
TYNEMOUTH Elizabeth Morton and Joseph Hall, by Banns, married 14th of September 1803
EARSDON 2 September 1806, Elizabeth Morton and George Nicholson, Both of this P. [She age 21, widow + he age 21, widower. Bondsman: Thos. Clennell, Morpeth, Wit. Robert Pearson, George Pickering - Durham Marriage Bonds, 14/8/1806]
NEWCASTLE ALL SAINTS Elizabeth Morton, of this parish and James Fisher, of this parish, by Banns, married 16 August, 1819. Wit. Peter Higham, Jonan. Scott, John Thompson
LONG HORSLEY Elizabeth Morton of this parish, Spinster and George Hedley of Bower Shield, parish of Elsdon, Bachelor, by Lic. with consent of parents. Wit. John Hedley, Henry Morton
NEWCASTLE ST JOHN Elizabeth Morton of this parish and John Donnelly of this parish, by Banns, married 8 August 1823. Wit. Thomas Donnelly, Henry Cockburn
Sadly, none of them are to a Murdy.
There is a possibility of a marriage in Scotland as he appears to have been a Presbyterian but I've done a search at Scotland's People and drawn a blank. I take it you've already done a search of Border Marriages.
Keep the faith!
Andrew