Right.
Maybe a local feed store or vet would let you place a flyer in their business.
Barn cats are always in demand somewhere. Some people let theirs roam 24/7 but others close them in the barn at night to keep them safe from predators like owls and coyotes.
Our barn cats seem to be happy. :-)
We had a shed with a cat door and in the winter, I ran an extension cord with a heat lamp for the couple cats we had and my black labrador. I made a kennel with straw for the dog and it was common to go out in the winter to see the cats bedded down with my lab.