Maureen,
I think you may struggle to get back much earlier than Francis Toal b c 1830. The records you need probably don’t exist.
I presume this is Frances & Sara in 1911:
http://www.census.nationalarchives.ie/pages/1911/Antrim/Toome/Brecart/125074/
You say that you don’t think Rose is Francis’s brother. I suspect he is her brother. (They both appear to have fathers named Francis anyway).
I looked up the birth of Francis Gribben, born in Motherwell. He was born on 6.12.1896 to George Gribben and Rose Toal who had married on 29.4.1887 in Duneane. (Scottish birth certificates helpfully record where and when the parents married). Rose died in Motherwell in 1902 aged 34. The 1887 marriage certificate tells us that Rose’s father was Frances Toal, fisherman. She was from Toome. Rose was born 1859 according to her marriage certificate. Rose’s marriage:
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1887/10799/5938303.pdfc
Francis’s marriage to Sarah McCormick which confirms his father’s name was also Francis:
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1879/11071/8050744.pdf
The only Toals I can see in the 1841/1851 census extracts were:
Mary Anne Toal who applied for a pension in 1916 (suggesting a birth c 1846). Her parents were John & Eliza Toal from Culnafay. 6 miles from Toome.
Thomas Kerrigan who applied in 1920 (suggesting a birth c 1850). His parents were James Kerrigan & Rose Toal and they lived in Taylorstown or Kilnock. Both of which are about 4 or 5 miles from Toome. The clerk reported finding James & Rose in Kilnock but not a son Thomas. However the subsequent entry does record Thomas so perhaps a mistake was made.
Sarah Kerrigan (married name McQuade) who applied in 1921. Same parents as Thomas above. Her townland in 1851 was Kilnock and the enumerator found a census entry for that with Agnes, Bernard, Mary, William, Rose, Thomas & Lizzie. Presumably all siblings. So this James & Rose must have married in 1841 or earlier. So they’d likely be born 1810 – 1820 or thereabouts.
I can add another Toal census extract taken from Josephine Masterson’s book on Northern Irish census extracts. Some census extracts are held in PRONI and are not included on the nli website (which was compiled from those held in Dublin). However they are in Mastersons’ book.
This is from the 1851 census and lists Bernard Toal head married 1820, wife Bridget Graham, James 19, Biddy 16, Rose Kerrigan (grand-daughter) 6. Absent on census night were Bernard 24 son, Mary 20, daughter. Deceased since 1841 were John aged 26. No date of death. The family lived in Duneane.
Bernard Toal is the only Toal farming in Duneane in the tithes in 1833. He could be related to Francis (b c 1830) but he doesn’t appear to be his father because he isn’t mentioned in the census extract. Plus Bernard doesn’t appear to be a family name in your particular tree. Hard to piece together at this distance.
If you are going to PRONI you could look up the O’Neill estate records. The land around Toome was owned by the O’Neills of Shane’s Castle. Their farming tenants estate books for 1829 & 1831 have survived (T1024/1 & T 1024/2 in PRONI). Those books show who was farming each farm, and also what lease they held. Many of the farmers held leases granted in the 1790s for 3 lives, so if the Toals were amongst them you might get a snapshot of who was there in the 1790s. Worth checking. (The rest of the O’Neill estate records were lost when their castle burned down in a fire in 1822).