The IFHS has advised that it has many Wicklow parish register entries available online (for a fee but freely searchable).
http://wicklow.brsgenealogy.com/.
From 1720 - 1800 there are about 30 Halbert baptisms, 13 Cotters, including Eaton Cotter in 1757, and 2 female Eatons. Over the same 80 year span, there are 2 Halpins, Maria in 1741 and Richard in 1799; there are about 70 Halfpenny and Halpenny variant baptisms and no Halpen.
Of the Halfpennys, there is no George, a very few Williams (1781, 1792) and James (1786, 1788), a few others earlier. The available Wicklow Town C of I parish records are among the oldest existing but these records are for all available County Wicklow registers, Catholic and C of I. The website publishes its list of sources.
I am becoming more confirmed in my belief that the Halpin family that we know of in Wicklow Town did not go there until James married Ann Halbert, whose family definitely did come from there. It is more probable that they came from elsewhere in County Wicklow that has poor surviving church records.
The Halbert family had property west of Ashford, at Kilmullin. The Wicklow Halpins could have come from near there, or from Bray, or even from near the Carlow/Kildare border. It may take a fluke to find out. Three of my Halpin family, in the 1800s, found brides in Carlow and I even then wondered if the family had some connection to that area.
However, William Halpin, paymaster, his son William of the Madras NI, and the George Halpin whose 1800 army discharge I reported a few days ago, all give their birthplace as Wicklow, George's even perhaps incorrectly showing Wicklow, Wicklow.
One perhaps remote possibility is that, before coming aboard the established church, they were Presbyterians. Evidence seems to suggest that the family of Leland Crosthwait were Presbyterian. (Search the IGI for "Leland Crosthwait".)
Of course they could have come from Queen's County but why did so many profess to come from Wicklow?
The fascinatingly evasive Halpin family.
Bill