Sounds like a fun trip!
Why is your grandfather so against international travel? Does he think it is unsafe? Or some other reason?
When you sit down with grandma and grandpa speak as if you're going (in a respectful way of course). "Hey guys guess what! I've been working at my part time job for x months to save up for a trip to Ireland!" Don't ask permission. No one asks permission to do something great, they seize the opportunity!!!
Show them that you've done your research. Show them an itinerary...where you're going and where you're staying. If they like your friends then tell Gparents that you're going to be staying with friends and/or they'll be showing you around. If your Gparents don't know your friends play that aspect down and show them you've booked a hostel (with cancellation protection, its a good idea anyway because sometimes friends' plans fall through and you get left without a bed). Show them your trip could be a benefit to your education. Show them activities you could do that relate to your major or intended major. Just another thing to play up...if your grandparents are religious or even semi religious Christians you could play up the religious aspect of it (going to see all the ancient churches etc). I'm sure you can think of other things...you know your grandparents better than me...
You could even make a PowerPoint presentation out of all of this...then you would look really serious.
Somehow I think your grandparents are not as against int'l travel as you think. Unless your G-ma got the passport behind your G-pa's back. There is no other reason to get a passport except to use it!!