The Centre for the Study of Historic Irish Houses and Estates at the National University of Ireland, Maynooth is currently carrying out research on the topic of Famine-era assisted emigration from Strokestown, Roscommon to Canada. The focus of this research are the tenants of the Strokestown Park estate who were sent from Ireland in 1847. In May of that year, 1,490 tenants left Liverpool for Quebec in British North America (Canada). They traveled on four ships: the Virginius, Naomi, John Munn, and the Erin’s Queen.
Unfortunately, before 1865 there are few passenger lists for immigrants coming to Canada. However, sources such as the Filby's phenomenal Passenger and Immigrant List Index (available on Ancestry.com) can help to fill the void. Library and Archives Canada also has a useful webpage about immigration before 1865.
Have you been able to trace your ancestors back to a May 1847 arrival in Quebec on one of those ships? If so, your next trip could be to county Roscommon.
To learn more about this assisted emigration, you can consult a news article from early May on the Journal.ie website.