These are his real-estate holdings, listed in Griffith's Valuation of 1858, Ireland's first systematic government valuation of real property.
46 acres and £42.25 valuation may not sound like much, but they mark him as a fairly wealthy man for the time and place; at least middle-class. Griffith's does not let one easily identify the house numbers. However, it seems pretty clear the Conyngham St. property was the one shown in the 1832-1846 Ordinance Survey map; nothing else fits the description. Note everything is leasehold; the Worshipful Company of Drapers and the Church of Ireland owned everything, back in the days before land reform.
We can get a broader look at the real estate using the Griffith valuation map.
All of these were confirmed to be the real William by examining the valuation revision books at PRONI. The Ballygruby holding was transferred to William's son Michael and thence to James, between 1858 and 1863; the rest were inherited by daughter Mary between 1864 and 1874, a time period which spans his death. They were sold after her death in 1905