Sorry to hear about the loss of your partner.
The regulations for Rent Supplement state that before being able to apply you must either have rented privately for 6 of the past 12 months or have been assessed by the local authority and be on their housing list.
As you're already on the housing list, you are eligible to apply.
There are maximum rent limits based on family size and location - the maximum rent limit for Co Limerick for a family with 1 child is €605 per month. This means you would not be eligible for Rent Supplement if the place you rent charges more than this amount.
Some areas set lower local limits, you will have to check that out with the CWO in the area.
If your only income is 217.80 (Child Benefit isn't counted) then you will be required to pay €26 pw towards the rent.
You should contact the local authority to see what they may be able to offer you.