I was wondering the same myself, and one day just decided to give it a go.
I popped the cover off the sensor, which caused the alarm to go off -"tamper alarm" - whoops. I do not have the alarm covered by monitoring (in fact it's no longer even connected to the phone line) so no problems there. I ran back to the panel and put in the "off" code as normal and it silenced it.
Of course the correct way to do this is probably to put the panel in "maintenance" or "engineer" mode or some such. I do not have that code, and since I have no contract with Eircom, I seriously doubt they will give it to me.
The battery inside the sensor was a regular 3 volt camera battery, widely available, although prices vary from one or two euro to ten euro or more! The code on my one was CR123A - I have a photo of the sensor with battery in place if you would like to see. You can get these batteries in a camera shop, or B&Q, or online (e.g. eBay)
I put in the new battery and replaced the cover. In my case, this didn't fix the issue, I think the sensor itself is probably broken (it keeps going off with SENSOR ALARM MEMORY alerts). But if you know your battery is failing, perhaps the above is of some help. Might be worth a try before you pay 100 euro plus for an Eircom callout.