Buying a bike in Ireland is simple, much the same as buying in the States.
Here is the process I recommend.
Search the local internet site, DoneDeal.ie - Ireland's biggest classifieds site
for used motorcycles.
Pick out the bike you like and shoot me or anybody else in Ireland an email with the link. I/we can check the bike out and finalize the deal.
What I have done in the past is just pay for the bike and wait for the wire transfer to come through from the new owner or, just wait for the new owner to come with cash.
It takes 2 weeks for the title to be mailed and when this arrives, green card insurance can be obtained.
I have done this for 6 US citizens and one Australian so far without any issues, either purchase or insurance.
This service is free and all I ask is enough to cover my expenses.