You'll need to do a bit of digging to see which options are available to you. Eir own all the phone lines into houses, so swapping to the likes of Sky will make no difference to the speed you're getting, but now instead of being able to report faults to the people who own the lines (Eir) you'll have to go through a middleman. It's bad enough without that if you ask me.
Ideally you want to get access to either fibre-to-the-home (only Eir and SIRO pull in fibe, so check both) or cable broadband (Virgin Media's offering).