this is a most unusual name and Irish records around 1800 and before are sparse. However I searched the name on a number of websites, firstly the Tithe Applottments done 1824 to 1837 as tax payable to the Church of Ireland the established Proststant Church http://titheapplotmentbooks.nationalarchives.ie/search/tab/index.jsp There are some Piers listed with two in Westmeath and on in Kilixby. This should be a relation of sorts as it is an unusual name in the right place.
I then looked at Griffiths Valuation done between 1848 and 1864 and got a number of Piers with 9 in Dublin, separate search for Dublin City and County. An Edward Piers is both a landholder and a landlord in Howth, this site comes with a little map which can be overlaid I understand (advanced computing for me I am afraid) but you can see it on modern maps, I should warn you that Howth is now very developed and up market area by the sea but lovely to visit.http://www.askaboutireland.ie/griffith-valuation/ Our ordance survey maps are here http://www.osi.ie/
Also see a Piers in Kilsallaghan, Dublin and this area is on the Dublin, Meath border so it coudl be the Meath you are referring to. Possibly pats of it are or were in Meath.
Also Dublin BMDs are online here and https://www.irishgenealogy.ie/en/ and I see a Pieres lady even in the 1600s section. Oddly most of these records are Church of Ireland if your man was a devout catholic. To find records at this remove indicates to me the family were of some standing in the community as most Irish people are lucky to get back beyond 1850 or 1800 at best.
There are 27 Piers in the 1901 census, appears only two families, one in Dublin and one in Armagh, you must select 1901 as default is 1911. See http://www.census.nationalarchives.ie/search/
I tried the online telephone book for Piers and it appears to only bring back Piers as a Christian name but one caught my eye was a name including Piers which is similiar to the name of one given in the Griffiths as a tenant of Piers so maybe that is a link, see http://www.eirphonebook.ie/
The lady's name Rielly is possibly Reilly which is a known spelling of the name or Riley as you give as an alternative.
Catholic Church records are now online here but without precise dates they are a very difficult read. http://registers.nli.ie/registers/vtls000633027#page/39/mode/1up Let me know if you would like the link to the Church of Ireland records but the Dublin ones appear above in Irish Genealogy.
If you wish to ask other questions please do.