There are Royce's in Galway East 43 births recorded and 17 in West Galway. In the 1850's the Griffiths Valuation took place, it name owners of land, their tenants and their sub-tenants.There were 23 Royce's listed names John, William, Charles and Mary. These can be seen at www.failteromhat.com
Is there someone in particular you are looking for. Galway has no bmd data base, however, the website www.igp-web.com
+ Galway has loads of information.
You can use the www.familysearch.org
website if families moved to US,UK, Canada as the 1880's census for these countries is there. Under 'search records' a 09/2009 PILOT project has been put on line. You can do all kinds of things with this website, it carries death records after 1864 and estimated year of birth from date at death. This works well for people who stayed in Ireland. There are birth records and marriage records with the registration districts (see www.from-ireland.net
for divisions of Ireland)also passenger lists and early to late US Census records.
I have at home a CD from LDS which has been replaced by the PILOT but the CD records parents names as well only those born between 1864-1875 are present, so I could find you Royce families/children within those dates.
'genealogy for fun'