I just recently got into Flogging Molly and The Dropkick Murphys. I really like the sound but I prefer their lighter songs, the ones without the frenetic fiddle and such. Are there any bands out there that I should be listening to that has the Irish punk sound but not quite so frantic?
Try Luke Kelly & The Dubliners. ETA: Or, if you like, just The Dubliners.
A good midway point between Flogging Molly and Dropkick Murphys, and truly traditional Irish music, would be The Pogues, who released a half dozen brilliant albums in the 80s. They had definite punk rock influences, but a much more authentic sound. (They were really Irish, unlike Dropkick Murphys, which is a good start.)
I was all set to recommend Flogging Molly, but I guess you’ve got that covered. For something a little less rocky, I also enjoy Gaelic Storm.
You could also look into Black 47.
Good choice. Pick up Red Roses For Me by them if you want the REALLY Irish sound. Each album got a little less traditional. Rum Sodemy and the Lash (my favorite) is a great album with a bit more punk rock in it. *If I Should Fall From Grace with God * (arguably their best album) is signifigantly less traditional sounding but still awesome.
Since you’re a guest and you can’t search, here are a few other threads that might be helpful (notice I said might!):
Recommend me some Irish folk musicians.
Ask the Person who knows a lot…
These are good recommendations. I would add Peace and Love as another decent record.
I also surprised no one mentioned the Chieftains. They have a huge catalog of really good, authentic Irish music.
Seconded on both counts
Thirded.
Other choices might be Patrick Street, Cherish The Ladies, and Niamh Parsons.
Maybe they are more Scottish but I recently got Casualties of Retail by the band called Enter the Haggis that I really like.
Filthy Thieving Bastards is also quite good. And on the Scottish front, check out The Real MacKenzies.
I know you didn’t ask about traditional Irish music, but you might be interested anyway. The two biggies in Irish trad are Bothy Band and Planxty. Patrick Street, Altan, and Solas are three contemporary heavyweights. Patrick Street’s Kevin Burke was a Bothy for years. I’ve never really liked the Chieftans—always thought they lacked gravitas compared to, say, Bothy Band, who were nothing if not soulful.
You could try The Fenians.
We are huge Pogues fans in my house- If I Should Fall From Grace With God is the best album, IMHO. My 5 year old likes Thousands are Sailing and Turkish Song of the Damned, and my 7 year old just named an undead WoW character Pogue (but then again, “vomit” was taken!).
I’ve always been a big fan of Tommy Makem & The Clancy Brothers.
Well, I was all set to recommend Gaelic Storm, but I guess you’ve got THAT covered! 
Did we remember to mention Stiff Little Fingers? Pretty punky and less identifiably “Irish” at a casual listen but fun and the influence is definitely there.
Before this thread goes under I need to mention Pat Kilbride. My parents used to listen to him when I was really young, and I always thought he had a great voice.
I just went and saw the Dropkick Murphys. They really put on a raucous kickass show. It’s been 10 years since I’ve seen such a humongous and dangerous mosh pit. Kilts, Celtic tats, Larry Bird jerseys and mohawks. Yeah, they’re a bunch of racist assholes from Boston, but they sure know how to put together some non-stop frenetic entertainment. Good replies, though, I gotta get some Pogues in my collection.
“The Boys From County Hell” are brilliant!