Do you know what religion Hugh and Catherine were? Have you got there marriage record?
Non Catholic marriages were registered from 1845 but Irish civil registration of Catholic marriages and all births and deaths did not start till 1864. I had a quick look at the civil records on http://www.irishgenealogy.ie for a marriage of a Hugh Thompson and Catherine Ward 1845-1859 and did not see one. This could be because they were Catholic or alternatively they married before 1845.
So you will need to consult church records in tracing the family. If they were Catholic you can check the church registers at https://registers.nli.ie/ There is no name index there but you can filter your search results by date and event within a parish. Alternatively you can sign up for a free account with FindMyPast and use their name index to the same record collection, labelled there Ireland Roman Catholic Parish
If you have an Ancestry subscription the same name index with the same errors is available there. Locating their marriage record may provide you with at least the name of their fathers. However as there was no standardisation of Catholic registers at this point there is no guarantee that this information is there.
Irish newspapers can be found on two main sites, neither of them are free. Irishnewsarchive.com is based in Ireland and is currently offering a large discount on subscriptions but the offer closes next Sunday night Irish time. Other newspapers are available through the British Library Newspaper collection some libraries offer access to this collection. The British Library Newspaper Collection is also available to some subscribers to FindMYPast.
The information on the discount offer is available at http://www.irish-genealogy-toolkit.com/Irish-genealogy-special-offers.html