The assistant shop manager of the Victoria Road branch, Lorraine, arrived for her morning shift to find the black bin bag on the doorstep - not an unusual occurrence.
However, she soon realised the bag contained something alive and opened it to find a young female cat with her two male kittens in a carrying basket.
A note with the cats said 'My name is Simba. Please find us a nice home.'
It is unknown how long the cats were left outside the shop early last week on an extremely warm day on the coast without any water.
Lorraine gave them a drink and took Simba and her kittens to Alma Vets for a health check with all three doing fine.
Nicola Byrne, branch administrator, said: "The mum is so small and a similar size to her kittens. She has now been neutered and the kittens have been weaned. It is a sad situation but all three will be available from next week for adoption (Monday June 26).
"We would remind people that this is not the way to give away unwanted pets. Owners should speak to a rehoming officer or look online to find the best way forward."
If you are interested in adopting one of the cats, or all of them, contact the RSPCA cat adoption team on 07926364633.
Information for owners with unwanted pets is available at https://www.rspca.org.uk/adviceandwelfare/pets/unwantedpets