The information you found on Brian Lawson's site is correct. I have checked it with parish records:
St Mary's R.C. Church( foundation stone 1857 consecrated 1859, any records you find before that would be St. Francis Xavier

10 Jan 1871
Patrick McCluskey,of New Bond St. Douglas, son of Owen McCluskey, married
Fanny Kayes, of Chapel Row, Douglas, daughter of John Kayes
Witnesses Thomas Gallagher (Chapel Row)
Ann Waterson (Lord St)

Their children baptised at St Mary's:

29 Mar 1872 John Henry McCluskey, godparents Henry McCluskey & Emily Collins

18 Jan 1874 Bridget McCluskey, godparents Joseph & Catherine Simpson

16 Jan 1876 Catherine McCluskey, godparents Joseph Simpson & Mary Ann Doyle

There is another John Henry baptised 1878, in the index, but I haven't checked it yet (parents Patrick McCluskey & Euphemia Keays)

It could be the same family because quite often the priest would record the nearest name in latin, though I would have expected Frances to be Francesca. Also Keays could be spelt Keys, Keyes, Kayes etc.

On some records Owen is recorded as Hugh, Hughee, Hughan, so it can be quite confusing.

I am still trying to establish a relationship between my McCartan, McCartin, McCarten's who were living on the island at the same time, and the McCarthy, McCarty, McCarthagh's. They all appeared to come from County Down, whilst my McAleavey relatives came from nearby County Louth. Marie