I am an American citizen looking to stay in Ireland longer than my 90 day tourist stamp allows. I am wondering if it is possible to leave Ireland which is a non Schengen country to go to France, Germany or somewhere in the Schengen zone for a week or two and then re enter ireland for a new 90 day tourist stamp?
The strategy of 'channel hopping' to get more leave is both legal and widely used, so yes, it's possible. Most people don't spend a week however, they return on the same day.
The answer is not complete without mentioning the risk. Upon returning to Ireland, you will have an interview with the Garda and you'll need to explain the purpose of your visit. If they notice that you are building up a life in Ireland or that your activities are not consistent with a tourist, you will get detained and bounced (either to France or the US depending upon their own discretion, flight schedules, and so on). On the 3rd hop, the estimated chance of getting bounced is about 97%, once that happens your travel in the CTA is finished for a while.
But indeed, it's a very convenient and economical way to get more time to visit and enjoy Ireland.