I am trying to find more information about an article that appeared in St Catherine's Journal, Ontario, 10/9/1859. The article was about the funeral of a child of an Oswego (New York) Irishman. (I'm trying to find the name of that gentleman.) Do you know of a good way to find a reprint of this paper?

If the newspaper was microfilmed you should be able to reprint the article. Head to your local library and ask if they have "Union List of Newspapers Held by Canadian Libraries" published by the National Library of Canada. It gives a listing of the newspapers available.