The best way for you is probably for them to accept a credit card reservation or payment. This protects you from a range of problems. It may not be something you are worried about - it's saved me in the past when I dealt with an apartment rental company that went out of business shortly after I stayed with them. My CC company refunded the security deposit (and hinted that they suspected other, broader problems with the company in question).
You'll have to ask the people you are dealing with if they'll accept an AIB cheque. My feeling is that they won't be keen - it'll take weeks to clear, and probably cost them into the bargain.
If a CC payment isn't an option, then a direct interbank transfer is easy. You'll need their bank account details in IBAN format, and their bank's code in SWIFT format - ask them to ask their bank for this information. You can use AIB's online banking to send the money if you are setup for online banking. According to their website, there is no charge for normal (1 to 3 days settlement) transfers. "Urgent" transfers cost €12.70, but I can't see what the difference is - the settlement period appears to be identical to standard.
The direct interbank transfer leaves you with no recourse should you have a dispute over the refund of the security deposit. AIB will not be willing to listen to any request to reverse the transfer once it has taken place. Probably not a big concern for you, but worth knowing I guess.