Bus Eireann offer a direct route from Busaras to Ikea for 25 euro. I think that's a bit expensive considering that it only runs once a day. It leaves Dublin at 10:00am and comes back from Belfast at 5:00pm. However, we reckon that there would be plenty of storage space on the coach, down below for any purchases made that day.
You could take the train. It's a bit more expensive at 38 euro roundtrip, but you'll knock at least an hour off your travel time and it runs every couple of hours. Not to mention the seats are much more comfortable and the views are to die for. Though, there isn't as much storage. You'd really only be able to take home what you could carry with you (kitchen accoutrements, textiles, picture frames, maybe the occassional bit of small flatpacked furniture).
We thought about hiring a van. Unfortunately, you have to have a full license or know someone who does. If you do, you can get a van for about 100 euro/day depending on the size. This is fairly reasonable, because Ikea charges 100 pounds per trolley load to send it down to the Republic. Bringing all your purchases home with you is an added bonus of hiring a van.
Of course, if none of those options tickle your fancy, you could always hire a private helicopter, use a speedboat, or perhaps walk.