British Newspaper Archive (BNA) database.
So far, the online holding for this paper consists only of 52 editions published in 1837, but it will eventually extend to 1872.
The British Newspaper Archive holding of Irish publications is fast approaching 100 titles, making it easily the largest online database of historical Irish newspapers. Subscriptions are available at £12.95 monthly or £79.95 annually.
The entire Irish holding can also be accessed on FindMyPast with an Ireland or World subscription. If you are currently actively engaged in Irish family history research, you may find this route more cost-effective.