Hello Kathy, I am looking at old querie and there is no record of that birth or any other children to those parents, the parish probably did not or has not got records at that time, a lot have and many havenot. Catholic Emancipation came about in 1829 but it did not deter many parishes from having earlier records.
I did find children born in the parish of Shanagolden to a Madigan / Downey couple but not your but may be related as i see a Margaret Downey as a witness to Daniel Madigan. Found 3 Madigan / Downey marriages but around 1840 so too late, but all in Limerick, I looked at an adjoining parish to Shanagolden (Loughill) and records there do not commence until about 1850 so could be there etc This site has church reocrds and you can see the parishes and when records began. https://registers.nli.ie/ ;
There are numerous county Facebook groups doing genealogy and DNA, usually separate if you want to give it a go but if there are no records there are no records unfortunately and the names are common enough in Limerick, you can see surname distribution for free on this subscription site if interested https://www.johngrenham.com/surnames/ ; a subscription is required to go further.
Good Luck
Pat
