where can i drop off cats in buffalo,New York

We decided to occasionally house a stray kitten that was left near backyard last year. The goal was for one of our family friends to come and adopt it by it never happened. Now this is a street cat and often runs outside and came and has since had kittens. We’ve attempted to drop them off to shelters but I’ve been told there full. Please my family does not have the capacity to care for this cat or its kitten. Please let me know if place accepting kittens or anyone who’s interested in adopting them.