Statutory birth registration didn’t start in Ireland till 1.1.1864 so you won’t find a birth certificate for Matilda (or any other children born before 1864). You may find their baptisms but the records are probably not on-line.
Taughboyne Church of Ireland has baptisms starting in 1820; the PRONI guide to church records lists 4 Presbyterian churches in the parish: 1st Ballylennon baptisms 1829-39 & 1861 onwards, 2nd Ballylennon no baptisms, Monreagh baptisms 1845 onwards & St Johnston, baptisms 1838 onwards.
There are copies of all the above records in PRONI, the public record office, in Belfast. A personal visit is required to access them. Access to the records there is free. This link explains what records exist, parish by parish:
If you are unable to go yourself, you could employ a researcher. Researchers in the PRONI area: http://sgni.net