The article Two Hundred Men at Tennis: Sport in North Dublin 1600–1760 (Maighréad Ní Mhurchadha) appeared in the Dublin Historical Record, Vol. LXI, No. 1 (spring 2008), pp.87–106. There are a few mentions of 'tennis', by which we should understand 'real tennis', in this article:

Although George Creichton had a soft spot for the Palesmen — at any rate he preferred them to the Ulster Irish — he strongly disapproved of their behaviour, for, having attended Mass in the morning, they spent all their time, as he said, playing tennis and drinking, piping and dancing. Particularly striking was his comment that he had observed above 200 able men together playing at tennis, an early indication of the interest which Fingallians had in sport. [p.87]

Rocque's map, published in 1756, shows tennis courts at Barrack Street in the north city.... [p.88]

A year later [1758], however, the lord mayor 'ordered the flags to be dug up of two tennis courts in Dame Street and two ball places in Barrack Street as public nuisances'. These 'ball places' were probably the tennis courts shown on Rocque's map though the wording of the newpaper report hints that they were no longer used for tennis. [p.88]

If we go back to the year 1612 [...] In its meeting on the second Friday after Easter in that year the Dublin civic assembly decreed: It is further ordered and agreed, by the said authority that every apprentice, journeyman and every other of the age of fourteen years or upwards, which shall be found playing at ... tennis ... or any other unlawful games, within any street of this city or suburbs of the same upon Sundays or holydays, shall presently be taken by the aldermen, deputy aldermen, and constables of every ward, and be committed to the Newgate, there to remain for the space of twenty-four hours without bail... [p.96, block quotation in original rendered as italics here]

Tennis was popular with all classes even before 1642. An argument between Christopher, earl of Howth and Sir Roger Jones which took place on a tennis court in Dublin ended in tragedy in 1609 when a man called Barnewall, a kinsman of the earl, was killed. Tennis was one of the sports mentioned in the decree of the Dublin civic assembly in 1612. Tennis is also mentioned in the poem 'Purgatorium Hibernicum', written about 1664. Later, in 1673, Bennett Arthur of Cabragh bequeathed 'three houses and a tennis court in Winetavern Street'. [pp.99–100]

Summarising the state of sport in north Dublin there is some reason to think that, by the end of the period, the authorities and establishment figures were beginning to wrest control of sport from the community. The destruction of ball places in Barrack Steet in 1758 ... lead to this conclusion. [p.102]

Many thanks to Roland Budd for bringing this interesting article to our attention.