Hello Aileen,
In many instances siblings of emigrants remained in Ireland. If they were still in Ireland between 1848-64 then you may be able to establish where the emigrants lived. There are still a reasonable number of families who are in Ireland today who are descended from those siblings who remained in Ireland. I had lunch with an old friend (slightly younger than I am) on Sunday who like myself was born in Ireland. He's still finding living relatives that he didn't know about when he was many years younger. It amazes me that some twentieth century mums and dads kept quiet about relatives and have left their children to meet strangers (who are related in some way) at family funerals.
Don't give up the search. I've read about members of the UHF giving talks in England telling people that if they don't know a family's denomination and the parish where they lived they've no chance of filling in the gaps. That's not one hundred per cent true ... the best thing you can do is keep asking questions as many of the answers are out there somewhere.
If people hit brick walls one of the best things they can do is visit Ireland and not only visit the archives but also get out and about and talk to people.
Your family arrived in Australia in 1857 ... six years after the Valuation took place in Co. Tyrone. Have a look at the extracts on John Hayes failteromhat.com website. There are two John Verners but there may be other names that you recognize.
John Verner, Carnteel
John Verner, Annaghmore, Aghaloo
As well as having a look at the Valuation
click here to have a look at the Castlederg New Cemetery Burial Records ... Information kindly provided by Mervyn Catterson. You'll see that there are several people named Scott and Verner on the list.
Christopher