James Gilmore and Margaret Kilroy "Foxford parish in or near the town of Cloongee"

My mother's parents were from parishes just to the east of Templemore, and I've searched many of the local parish registers, but as Roger noted most do not go back far enough for the baptsms which you want.  However, you might be able to find a marriage record for James and Margaret in the registers for either Swinford or Toomore (both of which adjoin Templemore), since they go back further than the others.  People were sometimes baptized or married in a nearby parish which already had a church in the early 1800's, when many Catholic churches were newly being built or rebuilt.

I have no known Gilmore relatives (though we're probably still related, at least distantly), but I happened to note down a James and Mary Gilmore acting as witnesses to a marriage on 15 July 1839 in Toomore.  There could be other Gilmore records there which I didn't note down, since I was looking for other surnames.  Here's a link to the Toomore marriage registers (same NLI site as the one to which Roger directed you), and you'll see an interactive map there which allows you to move easily to other parishes nearby:   https://registers.nli.ie/parishes/0131

In irish, Cloongee is Cluain Gaoith, which looks as though it means "estuary meadow" ("cluain" definitely means "meadow", but there's apparently some debate about the other word, which is close to the word for "wind", but not in the right form to make "windy meadow").  You can find more info about Cloongee at this link:  https://www.townlands.ie/mayo/gallen/templemore/toomore/cloongee/

In case you're interested, the surname Gilmore in Ireland has two separate origins.  One "clan" originated in Ulster, and the other originated in what is now Sligo.  Templemore is near the Sligo border, so you're likely to be descended from that "clan", although there were many people who came to Mayo in the 1600's form Ulster.  According to MacLysaght's Surnames of Ireland, the Irish form of the Ulster surname is Mac Giolla Mhuire ("son of the devotee of [the Virgin] Mary"), while the Irish form of the Sligo surname is Mac Giolla Mhir, which seemss to mean something like "son of the devotee of the lively one" (no further explanation was given).  Surnames of Gaelic origin are almost always based on the name or nickname of, or a characteteristc of, the family ancestor (real or purported),

Thank you both for such prompt and helpful replies. I was at a loss to know where to look next so I appreciate your information and suggestions