As with so many things the answer is "it depends".
If you look here you'll see that Irish rental income is reckonable for PRSI purposes: http://www.welfare.ie/EN/Publications/SW74/Pages/4DoIpayPRSIonallincome.aspx
A PAYE taxpayer filing a Form 12 with a small amount of rental income is not charged PRSI on it, as all they receive is a P21 balancing statement.
A "chargeable person" taxpayer filing a Form 11 with the same amount of rental income on it will be charged PRSI, because their return actually causes an Assessment to issue. The ROS offline Form 11 doesn't calculate PRSI on rental income (of any level) if the only other income is from PAYE employment, but if there is Case I income, it charges PRSI on the rental income. This looks like a bug in the software TBH, and I'm not sure whether the Assessment that would issue would agree with the ROS offline calculation... I'm going to look into it on Monday and report back...