It's a main linehaul route for all the big carriers, TNT, DHL, FedEx (they all have depots in Cork), along with loads of smaller domestic only carriers.
You'll get contact details online, or in the Golden Pages.
Couriers would work out too expensive for heavy items such as tiles. Best to try someone like Murphy Transport or Irish Express Cargo - not sure if they do one-off domestic work but worth a phonecall. You could also try Irish Removals based in Douglas - they do regular runs from Cork to Dublin and could include you in a part load?