Hmm. I think what you need is to find some kind person who is planning a visit to the Scotland's People centre and would be willing to look at all the Eli*abeth M*kay births until they find the one born on 10 December.
(You did mean that she was born on 10 December, married on 10 September and died on 6 March? Not 12 October, 9 October and 3 June, which is how an American reader would interpret those dates? It's alway a good idea to spell out the month when quoting dates, to avoid possible confusion.)