incheguilleagh

DJ:

I assume Lucy was Roman Catholic?

There are many Leary/O'Leary baptismal records in the RC parish of Iveleary (Inchigeelagh). However, no Lucy O'Leary records. Did Lucy have another first name? Any siblings? I assume you don't have parents names?

Roger McDonnell

What Roger said about how common the name O'Leary is in that area is correct.  In fact, the name of the Catholic parish of Iveleary is actually based on the O'Leary (in Irish, Ó Laoghaire) surname, which is believed to have originated in or near that very parish, although it is now quite common in all the surrounding parishes as well.

The parish records which are available online go back to 1816, and can be accessed at this link:

https://registers.nli.ie/parishes/0062

It is the name of the civil (or administrative) parish which is Inchigeelagh (with almost identical boundaries to those of the Catholic parish of Iveleary), although Inchigeelagh is also use at times as a name for the Catholic parish.  You can find more info about the civil parish at this link:

https://www.townlands.ie/cork/inchigeelagh2/

At that second link, you will see further links to the various townlands in the civil parish.  If you locate a relevant baptismal record in the parish register, it will usually tell you in what townland the family lived, and you can then use the second link I gave you to find more info about that townland, along with links to such things as relevant census records.

Her name was lucinda leary and had a sister called honora... they may have connection in clonakilty

is there anywhere in clonakilty i could search

The Catholic parish of Clonakilty (which includes the town of the same name) is about 12 miles southeast of Iveleary.  The parish records which are available online for Clonakilty go back to 1809 for baptisms, and you can access them at this link:

https://registers.nli.ie/parishes/0033

Since you have possible years of baptism, you could start with those years and then, if not successful, search the years either side of them.  In those days, people in rural Ireland often had no idea exactly when they were born (and no particular concern about their exact age), so all later records of birth dates or ages in censuses or the like should be taken as rough estimates with which to begin searching.