There were a couple of Spanish interventions in Ireland in the 16th and 17th century. The first, at
Smerwick was a catastrophe that resulted in a speedy surrender and then a massacre.
The second, at
Kinsale, was larger scale but was still plagued by issues- the landing site was bizarre, a significant number of troops and munitions never landed due to storms, their Irish allies Hugh O'Neill and Hugh O'Donnell took their time mobilising, there was dissension and a lack of co-ordination. Even if the Spanish won an initial victory, I'm not sure how long it would last- a Protestant England will not tolerate the Spanish for long, geographically it's far easier for England to exert power in Ireland, Spain will probably distracted on the continent sooner or later.
But, if you do have the Spanish and O'Neill/O'Donnell rout Lord Lieutenant Blount, some Irish will rally to them, maybe if you have Lizzie die a few years earlier the English might get distracted for a bit... Alternately, if you have someone different/less competent than Blount be sent over as Lord Lieutenant in 1600 you could tweak things to Spain's advantage (IIRC Blount was caught up in suspicions because of his association with Essex).
I'd imagine if you want Spanish success to have any permanence you'd probably want to flip the Old English as well as the native Irish, no idea how plausible this is.
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The 2nd and 3rd Armadas in the 1590s were also vaguely directed toward assisting the Irish rebels, not sure if something can come of this.
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Elsewise, is it possible to foment a scenario where Mary has children with Philip, and then said kid gets kicked off the throne of England but maintains control of Ireland (on the basis of shared Catholicism) either in alliance with a Spain under their half-brother Don Carlos, or in a Personal Union?
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However if you do manage to manufacture an independent Ireland then an alliance with Spain could happen relatively naturally. Such an Ireland would be Catholic and would seek an ally against the potential aggression of an England trying to reclaim lordship over Ireland (
especially if said England is Protestant). The main candidates would be France and Spain, but if this is the late 16th-century then Spain would be the better option- it's at the height of its powers(ish) and already hostile to England, whilst France is a basket case consumed by the religious wars.