Aiden is a pretty popular name, but I love it! Aiden Christopher sounds great. Of all the -den trends, I think it's the most traditional and the strongest one out there (as opposed to all the Kayden's and Jayden's). If it's a name both of you guys agree on, I'd definitely go for it.
If the popularity thing bugs you guys though (for a name like Aiden, it doesn't really bother me, unlike the popularity of other names like Makayla or whatever), what about (and sorry about this, but I'm not 100% sure they're all Irish): Finnegan (love the nickname Fin), Kearney, Dillon, Conan, Emmet, Fergus, Finbar, Lee (another definite classic, Lee Christopher sounds awesome), Lochlan (Loch could be a pretty cool nickname), Murphy, Pierce, Quinlan, Riley, Redmond, Edmond/Edmund, Ronan, Tadhg, Tierney, Tomas (always loved Tom), etc.
Still, Aiden Christopher is a good, solid name. Whatever you guys choose, good luck and congrats!!