Hi Lisa, I have been looking at various online stuff and my own copy of a catholic census for Tallenstown in 1837, there are a number of McCartneys but no Edward, there is a Widow McCartney living alone, the townland is Charlestown, there is no Edward listed in the Tithes either, this does not mean he was not there just he was not a holder of land over an acre or did not pay the tithes.
However I have looked at the marriage register, free online and the information does not give the parents names. only their name and the witnesses. You can see it here https://registers.nli.ie/parishes/0234 I have attached a snip.
I can find no other baptisms for a McCartney with a father Edward in Ireland from 1815 to 1825 and the name Priscilla would be very unusual at that time , however I see it as a sponsor on one of the baptisms. There are also a few in the Louth website below,
I can see the names you mention like Winters and Campbell in the area.
Records for Tallenstown baptisms only commence in 1817 and there is a 5 years gap from 1825 to 1830, marriages commence in 1804, I can see no record for an Edward getting married in Louth, Armagh, Meath and Monaghan, this may mean he got married in a church that does not have records at that remove.
Where did you get the information on her parents, there are a few Mary McCartney's born in Tallenstown but the one with the best date, Mary McCartney baptised 1st April 1818, to a Pat and and Anne Rowe or Roe, this would make her only 19 at marriage. If you have a death age it may assist but these are often guesses but the survivors.
There is a site on Louth here which lists many McCartney including some graveyards http://www.jbhall.clahs.ie/ there is also a Louth Genealogy FB page, apply to join, not overly busy. I see a little McCartney discussion on it.
If anything comes to mind please revert,
Pat