Well, I will be able to provide an answer, or at least a starting point, dealing primarily with the 17th and early 18th centuries. Irish folklore tends to sweep the entirety of this period into a single monolithic ‘Penal days’. In these depictions mass is portrayed as being exclusively celebrated at remote outdoor sites known as ‘Mass Rocks’, often accompanied with grisly tales of priests being murdered at the very altar by English soldiers. Mass rocks did exist, but as ever the reality is a bit more nuanced.
Post-reformation Ireland occupied a rather peculiar position within the ‘British Isles’. It was the only area of the Stuart multiple-monarchy in which the majority of the population was Catholic. However, the precise relationship between the King, his governors and his Catholic subjects in Ireland is something which could vary significantly throughout this period, both in policy and practice. This confessional division was a constant source of tension.
In spite of the fact that the Protestant Church of Ireland was established as the official state religion, the English crown proved utterly ineffectual in its attempts to promote the reformation in Ireland. This did not solely apply to the Gaelic Irish nobility, or the ‘lower orders’ either. The so-called ‘Old English’ nobility (descendents of the original Medieval colonists) also stuck to their ancestral faith too. This caused a serious headache for English administrators in their efforts to stamp out Catholicism.
Naturally this allowed for the circumstances which enabled the survival of Catholicism in Ireland broadly speaking (at least until the end of the 17th century), as well set the circumstances under which Mass was celebrated. Depending on the particular time period, as well as area this tended to be in one of two places. Where there was an influential Catholic landlord in a particular area, then Mass might be celebrated in private chapels on their estates. In other areas mass would be heard in private areas, or in specially built ‘mass houses’ (what were essentially very simple, rustic churches).
It’s not quite as straightforward as simply stating that it was illegal to practice Catholicism. Of course, there were periods of intense persecution during which mass rocks would have been used in some areas. Catholicism was not legally tolerated and so this isn’t to give the impression that everything was hunky dory either. In certain areas of Protestant control life could be incredibly difficult indeed. After Cromwell’s victory in the 1650s there was a period of particularly harsh suppression for instance.
However, the reality at local levels was often messier than government proclamations might suggest. At various times political expediency and economic realities meant that a kind of grudging toleration was the order of the day. What was law in name was not as often carried through with in practice. As a consequence people were still very much able to continue to practice their faith and continue to celebrate Mass.
If you want more of a deeper dive (but still fairly shallow in the grand scheme of things), with some specific examples, then on we go…