The second property will be assessed against you for the purposes of Rent Supplement.
It will be assessed on its capital value, which is the property value minus the amount of any mortgage on the property.
Once the capital value has been determined, it is assessed as follows (along with any other savings you may have):
Disregard first € 5,000 of capital value of property/savings
Assess next € 10,000 @ € 1 per € 1,000
Assess next € 25,000 @ € 2 per € 1,000
Assess remaining capital over € 40,000 @ € 4 per € 1,000.
The total is the amount of weekly means which will be assessed.
You will also have to meet the qualifying rules for Rent Supplement - more information here
http://www.welfare.ie/EN/Schemes/SupplementaryWelfareAllowance/Pages/RentSupplement.aspx