Mema,
If William & Maggie had a son born in 1844, as Shane’s information suggests, then that makes an 1847 marriage unlikely. (And there isn’t a Bell-Ferguson marriage in the 1847 records, as Shane and I can confirm). Their son’s birth in April 1844 points to a marriage in 1843 or earlier. Pre 1845 marriages are not in the statutory marriage records (which start in April 1845). To trace a pre 1845 marriage you need to know the location and denomination. Tradition was to marry in the bride’s church, so it’s her denomination then that matters.
Not all the pre 1845 marriage records have survived, and many of those that do survive are not on-line so tracing it can be difficult.
You say that William & Maggie had a daughter Martha Jane born 1873. I searched the births 1871 to 1875. There are 6 Martha Bells born in that period in what is now Northern Ireland. None has a mother named Ferguson. Also Martha’s birth in 1873 would be at least 30 years after her parents had married which makes it pretty unlikely (unless there had been a second marriage).
So I don’t think the above information is totally accurate and perhaps needs checking.
Statutory birth registration only started in Ireland in 1864, so for births before that (which I think is all their children) you need to rely on church baptism records. So you need to find the right church.
Catherine Bell married in 1868 in Orritor Presbyterian church. Her townland was Ballynasollus, and her father William was a farmer. Orritor Presbyterian church has baptism records from 1831 onwards. The only copy is held by the Minister, so you would need to write to him/her to see if there is any trace of the children’s baptisms. The church has no marriage records before 1845 so if that’s where the parents married around 1843, then sadly the records are lost. However as I say tradition was to marry in the bride’s church, and so they may have married elsewhere. You could try the local church of Ireland for example.
Griffiths Valuation records a William Bell in Ballynasollus in 1859. He had plot 19 which was a 12 acre farm. He died in 1873, aged 65 (so born c 1808, if the age was accurate).
The Will of William Bell late of Ballynasallus County Tyrone Farmer deceased who died 4 May 1873 at same place was proved at Armagh by the oaths of Richard Bell and William Dale of Ballynasallus (Cookstown) aforesaid Farmers the Executors.
William’s will is on-line on the PRONI wills site. It mentions his wife Maggie, 3 unmarried daughters Margaret, Hannah & Elizabeth plus 2 married daughters Rachel Glasgow and Catherine Calhoon, both of whom were living in Ballybriest. It also mentions a son Alexander who was evidently still a minor. So some of the children’s names tie in with your information but there are clearly some new ones, and no mention of any Martha Jane, who I suspect must be from a different family.
Elizabeth’s marriage in 1881 and Hannah’s in 1878 were both in Orritor Presbyterian which to my mind confirms it was the family church. Both gave their address as Ballynasollus.
This looks to be Alexander and family in 1901. The denomination suggests that at that date they were probably Brethren (often called Plymouth Brethren, though that’s not a term often used in Ireland).
http://www.census.nationalarchives.ie/pages/1901/Tyrone/Ballynasollus/Ballynasollus/1730413/
This is probably Rachel Glasgow (nee Bell).
http://www.census.nationalarchives.ie/pages/1901/Tyrone/Ballynasollus/Ballynasollus/1730405/
Maggie Bell nee Ferguson died 17.2.1897 aged 79 at Killary. She was staying with Elizabeth & Benjamin Sinnamon.
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_retu…
This is them in 1901:
http://www.census.nationalarchives.ie/pages/1901/Tyrone/Pomeroy/Lurganeden/1731214/
Hope this helps sort the family out.