DAB radios only receive stations from your local digital transmitter. The radio stations have to pay to have their programmes included in the local line-up. A commercial radio station in Ireland won't carry advertising targeted at your area, so it's highly unlikely that it would be available on your local transmitter. (Even RTE would find no commercial advantage from broadcasting on transmitters in the UK).
VHF ('FM') signals only carry over a very short distance, so buying a combined DAB/FM radio won't help.
The only way that you'll be able to listen to your favourite station is over the internet. When internet broadcasting first started, most stations used the 'Real Media' format, which meant that you needed to install Real Player to listen to them. Some stations still use this format but most stations now use a format which uses Windows Media Player (which comes with Windows). You simply click on the relevant link and Windows Media Player should open and load the stream from the required station.
The links for all stations in the Republic of Ireland can be found here:
http://www.ico.gov.uk/what_we_cover/data_prote ction.aspx
(See the foot of the page to check whether the station requires Real Player or Windows Media Player).
If you'd rather not listen to the radio station through your computer, you can buy special radios which connect to the internet. Simply search for 'internet radio' on sites like Amazon.
Chris