Flogging Molly is a bit of an unknown band. Typically, they've gotten overlooked I believe because they don't quite fit into any one category. Are they alternative? Not compared to alternative bands. Are they hard rock? Not really. Metal? No. Punk? Yeah, I think they've been lumped into the "punk" category. Consequently, they don't get much airplay.
Anyway, "Drunken Lullabies" is one of their better songs. I like it because it's quite upbeat and can help me both get pumped up or cool down if I've listened to a couple of hard songs in a row.