In the 1800s very few people in Ireland owned 'their' land- most were tenants. Griffith's Valuation (the full, printed version) will give names of both the tenant and the landlord (immediate lessor). For County Londonderry Griffith's Valuation was c1859.
PRONI has just recently put the Will index information on their website (
www.proni.gov.uk).
Census details were collected every 10 years just like England but unfortunately most of the early ones were destroyed by fire or deliberately pulped once population statistics for each townland were noted. First complete census for all of Ireland is 1901. 1911 and 1901 census are being put online (just started last month with 1911 Dublin)- see here for details:
www.census.nationalarchives.ieHowever, 1831 census for part of County Londonderry did survive (Barony of Coleraine, City of Londonderry, Barony of Loughlinsholin, Barony of Tirkeeran) but it was more a religious census listing townland, head of household, number of males and females in household, and how many were E.C. (Established Church i.e. Church of Ireland), Presbyterian, R.C., other.
The main source of family information in 1800s would be church records. In order to find them (of they survived) you need to know religion and where the family lived (parish if not actual townland not just the county).