You are tiptoeing at the abyss of Irish pre-history. The truth is that the number of records which survived prior to abt 1840 gets increasingly sparse as you go back in time.
There are two possible sources which MAY have earlier records which weren't consulted when the current databases were created. The first is the National Library of Ireland.
The NLI made microfilms of nearly all surviving parish (RC only?) registers early in the 1920s. Some of the originals have succumbed to time and happenstance since.
The second was a series of volumes which redacted info from earlier parish registers. One (of many) of these was published in 1910. Thus, its redactions predate the NLI microfilms and the Four Courts fire debacle of 1922. While published by the church(es), copies should exist at the NLI. Contact the NLI's reference librarian for these arcane, obscure tomes.