In addition to purchasing a Retirement Annuity with their pension fund, the OP is considering purchasing an annuity outside their pension, using savings that have already been subject to tax at source. I gather the latter is referred to as a Purchased Life Annuity (PLA).
@ClubMan what is your reference for the statement that the tax treatment for both Retirement Annuities and PLAs would be the same? Note that OP is not asking about funding their pension contributions from net tax savings.
This sounds plausible to me for OP's situation:
If you were to put post tax funds in a purchased life annuity (if anyone still sells them), part of each payment would be considered return of capital and part would be income. The income part is taxed at 20%.
But I cannot find a definitive Revenue reference, as it's an unusual situation (and as Fortune also said, such annuity products may no longer be readily available in Ireland). Although this seems relevant:
No 39 of 1997, Section 788, Revenue Note for Guidance
www.charteredaccountants.ie
Certainly, if the annuity payment was a gift or inheritance, it would be
taxed in a fairly unique way. So that's a third type of annuity you could receive payments from ...
It seems overly pedantic to pretend that the OPs definition of 'income' in their question on taxation of 'income' excludes the capital portion of the annuity payment. They are obviously aware that true income is assessable for income tax.
Bonus question: it should be possible to use a tax free retirement lump sum to setup a PLA. Should retirees purchasing Retirement Annuities be advised to consider this?