Go to your local Garda immigration officer (if you're in Dublin go to the Dept of Justice building at Burgh Quay) with the passport and evidence that you can support yourself for the extra couple weeks and ask for an extension. Do this before your current permission expires!!!!! It's pretty much at the discretion of the person you speak to whether or not they will give you an extra couple weeks, but it has been done.
If that doesn't work, fly to France.
I'd be really careful, if I were you. If you are accused of attempting to bypass immigration law (which, if we're honest, is what you are doing) you'll end up in a whole lot of shit. At the very least you'll have a difficult time getting in to the country in the future -- but you could end up being refused entry or indeed they may come down on you like a ton of bricks. Immigration is a super-hot issue in the UK and Ireland these days.
Any immigration official worth his/her salt will notice that you've left the country on the last day of your tourist visa, only to return a day or two later for a fresh 90-days stamp. You MIGHT get away with it, but I wouldn't recommend it.
The trouble is, if you start talking to immigration about 'needing to extend your stay by 2 weeks', you're starting to sound like less of a tourist, and more like you're shacked up with your b/f, or are working, which may arouse suspicions.
Why don't the two of you head over to the UK for your remaining fortnight, or grab a cheapo ryan air flight somewhere nice in Europe -- that way you have no complications
Wasn't your passport stamped when you entered Ireland? How many days did you get there? Not having to apply for a visa before your visit does not mean you don't have a visa, with a US passport you are part of the visa-waiver plan, which more or less means you get your entrance visa upon arrival without hassle or any fee.
If you were given 90 days in your passport, you should leave once they are up to avoid trouble.
#13 Ireland doesn't have a "visa waiver plan". It simply doesn't require visas for nationals of particular countries, including the US. For more information see www.inis.gov.ie.
OP you won't get in any trouble by going to Garda immigration before your current stamp expires and asking if they will extend your stay by a couple weeks. They may not do so, but you won't get in trouble for asking.
