From what I know of study abroad programs, students either go for a summer term (usually a month to six weeks) or for a semester. I've never heard of a program where you only go for a month anytime other than in the summer, since it would interrupt other classes.
Your best bet is to start by talking to someone from the study abroad program for your school. If you go to a larger school, there should be a study abroad office. If you go to a smaller school, the program may be run by a faculty member. Most schools have a set of classes they offer in various countries; if your school doesn't offer a program in Ireland, they may be able to help you arrange a study abroad trip through another school. You'll have to make sure the credits will transfer, though.
I encourage you to go in an immersion program if possible. That means you'd be going to an Irish school with Irish students, not just with a bunch of American students, which I think prevents students from getting everything from the experience that they can.
A semester abroad costs more than a semester on campus. $4000 isn't an unreasonable fee, from what I've heard from students I've had who have studied abroad. If that money covers living expenses or side trips (students typically have long weekends when studying abroad to give them time to travel), it may be a good option.
The key is to plan ahead. I'd say it's already too late to plan to study abroad in the fall, but your school might offer a winter term, or else you can make sure you get the last of your graduation requirements out of the way in the fall so you can go in the spring.