2nd try , in case anything is useful for you.
1660s Ulster Hearth Rolls see
http://www.billmacafee.com2201 173 L'Derry N. W. Liberties of L'Derry City of Londonderry Outside Walls at the Bishop's Gate Without Bishop's Gate William Fergison Ferguson
3431 1403 L'Derry N E Liberties of Coleraine Ballyrashane & Kildollagh Not specified Not specified John Fergisson Ferguson
1796 Flax growers of IrelandFerguson James Tamlaght Derry
Ferguson Thomas Tamlaght Derry
1851 surviving Census fragment. You found the Fergusons in the 1851 surviving census fragment
1858 I didnt know that Moys is in CARRICK civil parish by the time of
Griffiths valuation 1858 as earlier, it was in TAMLAGHT FINLAGAN
so another look at
1858 GV
http://www.askaboutireland.ie/griffith-valuation/ results for Carrick
Ferguson, John Townland: Largy
Ferguson, Joseph Townland: Ballyquinn
Ferguson, Joseph Townland: Moys
Ferguson, Matthew Townland: Ballymore
Ferguson, Rebecca Townland: Largy
Ferguson, Robert Townland: Carrick
1858 GV map Joseph Moys map ref 13 o
has modest garden valued at 2 shillings pa and modest house 8 shillings pa
I finally got map to load, I think 13A , an area whose northern boundary runs along the south side of the Glenhead northeastwards towards the Moys village, contains 13o as the 2nd dwelling in from the west end of a line of continuous dwellings, possibly labourers cottages.. Sadly the dwellings have gone and a long barn built southwards down the road that the dwellings ending 13p or 13q ran into.on their side thats points SW ards .
PRONI Valuation Revision Books continues above see
https://apps.proni.gov.uk/Val12B/ImageResult.aspxCurrent PRONI Reference: VAL/12/B/31/24B (1864 - 1882)
Joseph Ferguson still there and was checked in 1880
VAL/12/B/31/24C
hes there until 1897 where he is crossed out and Mary Anne Ferguson replaces him
in VAL/12/B/31/24D (1899 - 1915)
13Aa previous tenants Marcus Anderson >1901and Joseph Nichol 1906 crossed out and replaced with Robert Ferguson <1907 slightly bigger garden and dwelling
Mary Anne is still at 13o, so was Robert living with his aunt beforehand
in VAL/12/B/31/24E (1916 - 1929)
Mary Anne is replaced 1918 and after vacancy period by Mrs Moore
presumably you have tried the
1901 and 1911census - Moys is in the district called The Highlands
which includes
Ballydarrog
Ballymore
Claggan
Corlaragh
Culmore Upper
Dromore
Drumrane
Drumreighland
Largy
Magheramore
Moys
Sesnagh
Tartnakelly
Terrydrum
but excludes Moys three neighbouring townlands
Ardinarive to the west check parish for each later and for Ferguson
Carrick to the east check parish for each later and for Ferguson
Leeke to the south check parish for each later and for Ferguson
1901 has
29 in Moys (The Highlands, Londonderry) all Church of Ireland The family household in 1911 are now Presbyterian G A All the family could not read in 1901
Ferguson Robert 43 53 in 1911 General Labourer - Married -Annie 47 55 in 1911 House Wife -
children
Ferguson Annie 13 by1911 no longer living at home -
Ferguson Lavina 11 by1911 no longer living at home
Ferguson Margaret 9 by1911 no longer living at home
Ferguson Matilda 7 by 1911 can read and write
Ferguson Robert 4 by 1911 can read and write
{Thomas aged 8i n 1911 can read and write}
42 in Moys (The Highlands, Londonderry)
Ferguson Mary Ann 50 Presbyterian Cannot read - Not Married -
good luck onwards