Question

I am looking for Mary Maxwell born 22/11/1822 in Cuilmore Carrickmakeegan co leitrim Ireland

Answer 1

Do you have a profile for her?  Husband, parents, siblings, children?  

I should let you know that birth, death and marriage registrations were not required until the mid 1840's, although there can be some parish records or historical documents that predate that.  Women are particularly difficult to locate.

Cuilmore and  Carrickmakeegan are two different townlands, not  in the same place.  But they are both in the parish of Drumreilly. 

These are people in the parish who paid tithes to the Church of Ireland (Anglican) in 1834, all people had to pay tithes to the Church of Ireland, it didn't matter what religion they were.  You may find something if you look up the father's name and see if there is anything that tells you who their children were.   http://titheapplotmentbooks.nationalarchives.ie/search/tab/results.jsp?surname=maxwell+&firstname=&county=Leitrim&parish=drumreilly&townland=&search=Search

Answer 2

Wikitree has a well run one-name-study looking for Maxwells in Ireland, managed by Maria Maxwell.

https://www.wikitree.com/wiki/Space:Maxwell_Name_Study_-_Ireland