Banks are not currently required to open an account for anyone and can use residence as a reason not to. Having said that, most German high street banks will open an account with a Passport and some Irish utility bills (or preferably bank statements for your Irish bank). The likes of the Sparkasse will probably be the easiest as they are required to open accounts for anyone that wants one, even if they are not the sort of customer the other banks would want.
You will have to visit Germany in person to open an account with them.
You could try your luck with my bank, DKB.de, if you can at least read German. You can theoretically prove your identity to them using a notary in Ireland (or your own bank can stamp the forms if they will oblige!). Their target foreign audience is German expats though, so your mileage may vary! They have a bit of a reputation for refusing people even resident in Germany, but if you manage to open an account with them you won't be disappointed. Good service and absolutely no fees. You can even withdraw cash worldwide for nothing (even at those awful private ATMs in the states that charge you a few dollars..if you keep the receipt DKB will reimburse!).