PAWS in Seattle will give you a cat and it comes for a coupon for a free spay or neuter (often kittens are too young at adoption time). Of course the fee for adoption is higher than the cost of the surgery, so you are paying for it whether you use it or not.
There are often very cheap city/county options too: where I live its less than $30 for a spay/neuter + rabies vacc (significantly less than a private vet would charge).
Charge a high pet licensing fee if they are not.