Hi William, thanks for your message and interest in Ireland Reaching Out.
Yes, unfortunately it can be difficult when it comes to Ireland as so many records from the 19th century were either destroyed or didn't exist! However, there are a few places where you can try to search for information regarding the Gradys and Kanes.
Have you searched any of the land records pertaining to Ireland in the 19th century? These act as good census substitutes as there are no census records prior to 1901. The first is the Tithe Applotment Books, dating from 1823 to 1838. This might be the one of most relevance to you, due to the dates that the families emigrated. You can do a search of these records here:
http://titheapplotmentbooks.nationalarchives.ie/search/tab/home.jsp
The second is the Griffith's Valuation dating from 1848 to 1864, and might also be worth a try. You can find it here:
http://www.askaboutireland.ie/griffith-valuation/
Even if you could find some record of the families in these land records, it would confirm that they were in fact from Cookstown.
You could also try searching through Church records for the Cookstown area. Most Catholic records are held locally. One website which may be helpful though is the Irishtimes website. Here they give an overview of what records are available in specific parishes. To see what is available for the Cookstown/Desertcreight parish, follow this link:
http://www.irishtimes.com/ancestor/fuses/rcparishmaps/index.cfm?fuseaction=showidrecords&CityCounty=Tyrone&parish=Desertcreight&churchid=204
For Church of Ireland Records go to http://ireland.anglican.org/about/42 and http://www.nationalarchives.ie/
Do you know much about their emigration? Generally more information was given at the port of arrival rather than that of departure. If you knew where they entered the UK it may be a good place to find information.
Some websites that may be of help to you while doing your research are:
The National Archives of Ireland http://www.nationalarchives.ie/genealogy1/genealogy-records/introduction/
The National Library of Ireland http://www.nli.ie/en/family-history-introduction.aspx
The National Archives UK ? genealogy search: http://www.nationalarchives.gov.uk/records/looking-for-person/
and
The Public Records Office of Northern Ireland http://www.proni.gov.uk/index/family_history.htm
I hope that this information is of some help to you.
Kind regards,
Genealogy Support