Going back to the original query and noticing Dee Melodys help I took that further
http://www.askaboutireland.ie/griffith-valuation really does focus on the Dilworth /Dillworth population in Ireland before the 1860s, being in six civil parishes
ARMAGH    MULLAGHBRACK
ARMAGH    SEAGOE
ARMAGH    TARTARAGHAN
TYRONE    CLONFEACLE
TYRONE    DONAGHENRY
TYRONE    KILLYMAN 
These consisted of over 55 entries consisting of homesteads and a few just renting land The majority of some 40 focused into the civil parish of  of Killyman Co Tyrone 
There were others of course who escaped the Griffith valuation, there are 6 in Co Down just in the 1860’s as no doubt later Limerick
Analyzing them further for clues, my suggestions for further investigation include 
DILWORTH    GEORGE    TYRONE    KILLYMAN
DILWORTH    JAMES    ARMAGH    SEAGOE
DILWORTH    JAMES    ARMAGH    SEAGOE
DILWORTH    JAMES    ARMAGH    TARTARAGHAN
DILWORTH    JAMES    TYRONE    KILLYMAN
DILWORTH    JAMES    TYRONE    KILLYMAN
One can look up the date  eg George in the townland of Lowertown in Killyman has 13 good quality acres and a reasonable house valued at £1-15 shillings, compared to lowest worth 5 shillings per annum, or they are excluded from the listings
There were others of course who escaped the Griffith valuation, there are 6 in Co Down just in the 1860’s
So you need to check if anyone has copy of any surviving records church records eg familysearch .com, , I go to the PRONI website so for example for Killyman, their records are
KILLYMAN, COS ARMAGH AND TYRONE
C.I. Annaghmore
[see under LOUGHGALL]
C.I. Brackaville
[see under DONAGHENRY]
C.I. Killyman (Armagh diocese)
Baptisms, 1745-1871; marriages, 1741-1845; burials,
1745-1875; vestry minutes, 1756-1894; confirmations,
1837.
Baptisms, 1872-; marriages, 1845-; burials, 1876-;
registers of vestrymen, 1870-.
MIC583/33-35
In local custody
M. Kinnego
Baptisms, 1874-. (At Moy Church but earlier entries at
Armagh Church) In local custody
M. Laghey
Baptisms, 1830-. (At Dungannon) In local custody
R.C. Killyman
[Forms part of the Roman Catholic parish of
Dungannon – see under DRUMGLASS]
I cant help further , good luck onwards to all, terrific pics JimG