Mary Anne,
Not finding any passenger records for someone who moved to Canada in the 1840s is not unusual. It doesn’t appear that records were routinely required at that time. Quite a lot of emigrants from Tyrone left via the port of Londonderry. J & J Cooke there had regular sailings to Quebec and St John NB. Their passenger records for 1847 onwards are in PRONI D.2892/1/1-14 and on several of the usual pay to view sites. You might want to check them if you have not already done so.
The tithes only list people with land. It was compiled for tax purposes based on the amount of land you had. So to be in the tithes, in general you had to be a farmer or someone with enough land to be worth assessing. So a lot of the population are not in it. Obviously anyone living in a town, or servants, labourers etc are not listed. So to be in the tithes James Montgomery probably had to be a farmer. I searched the tithes for the entry you have apparently found but I couldn’t find a James Montgomery in Urney, nor could I find a townland named Drumnahan. There is a townland in Urney called Drumnaha but it is actually in the neighbouring county of Donegal. The parish straddles the 2 counties and Drumnaha is just across the border.
https://cotyroneireland.com/tithe/urney_tithe.html
I searched the tithes for Co. Tyrone and found 11 James Montgomery entries across the county. I suspect any one of those might be your family. Or none if he wasn’t a farmer.
I searched rootsireland for the marriage and William’s baptism but without success.
Statutory birth registration didn’t start in Ireland till 1864 and marriages weren’t registered before 1845, so there won’t be any statutory records of the Montgomery marriage nor of their children’s’ births. To trace them you need to rely on church records, not all of which have survived and not all of which are on-line. You also need to know the family’s exact denomination. If you aren’t sure I’d suspect Presbyterian or Church of Ireland from the surnames and the general location. The middle name of Crosby also hints at Presbyterianism. Tradition was to marry in the bride’s church after which she’d attend her husband’s so the marriage and children’s baptisms may not be in the same church.
James Montgomery is a common name in Tyrone. In the 1901 census there were 18. There were also 6 Sarah Huston/Houston. (Both spellings are found in Tyrone but Houston is more common).
All I can really suggest is that you look at where there were James Montgomery households in the tithes, and then search the church records for those parishes. It might also be worth looking in the same parishes in Griffiths Valuation which, for Tyrone, was compiled in 1859. If there’s still a James Montgomery listed then, it presumably isn’t your family and can be eliminated.
http://www.askaboutireland.ie/griffith-valuation/index.xml?action=nameSearch
Most of the surviving church records for Tyrone are in PRONI (the public record office) in Belfast. They are not on-line and a personal visit is required to view them. If visiting PRONI, take photo id to get your readers card.
