Familysearch has some Irish births for the period 1920 – 1930 but not all. In general, they are not on-line because they are less than 100 years old. (Similarly, marriages less than 75 years and deaths 50 years old are not on-line either). The records are open to the public, just not on-line.
Important to know which jurisdiction your ancestors lived in. From 1.1.1922 onwards the records for Northern Ireland are held by GRONI in Belfast, and those for what is now the Republic of Ireland are held by GRO Roscommon. You can contact both and ask for searches. (There are likely to be fees for that).
