Hi, I'm having pronblems with some new family members from Ireland.

Hannah Conway b, 1823, Galway, Ireland married Thomas Morley in 1849, Leeds.
In the 1871 census Hannah and Thomas appear with their three children; Mary b 1850, James b 1853, and Ellen b 1855,all born Leeds. Thomas Morley b.1831 (Hannah's husband) is also from Ireland...but it doesn't state where exactly.
RG10/4555 Folio 100 Page 14
Also in 1871 there is a Mary Conway b 1849, Ireland unm lodging with them....This,I believe is a niece of Hannah because she appears in 1851 as dau of Patrick Conway,b 1821, Ireland.
HO107/2319 Folio 454 Page 19
In 1881 Hannah Morley, now a widow is living with her married son, James Morley.
RG11/4520 Folio 152 Page 12
My problem....I can't find either Thomas or Hannah Morley, or any of their children (Mary b 1850, Leeds, James b 1853, Leeds and Ellen b 1855, Leeds) in either the 1851 or 1861 census...or Mary Conway either.
Are there censuses for Ireland for these years? Although I doubt that they went back and forth btn the births of their kids.??
And where should I start to search for records as to the parents and siblings of Hannah Conway? I haven't found anything on family search.
Hope someone can help, best wishes, Gillian