I'm curious - why doesn't your cousin want to have her spayed? That's really the best solution
To answer your question - you might be able to advertise on Craig's list that you are looking for an intact tom. Or if they have community bulletin boards at a nearby supermarket you could post a message. Be safe though. As far as breeders, they probably restrict their male cat's mating to the breed they're working with.
Is the girl a special breed? Is your cousin trying to become a breeder?
In my country, and with the breed that I breed, it's normal to go to other breeders and "borrow" their male for a certain fee. However, I know that in other countries they aren't that keen on it. So if your cousin has a breed she wishes to breed, she'll most likely need her own male, as well as a registered cattery etc. If she doesn't have any specific breed, I'm quite sure she won't be able to find a stud at another breeder. In that case, it's better to get her sprayed, so she doesn't have to go through all the hormones all the time - it's harmful for the cat, and the longer she is in heat without getting the kittens, the more she's at risk for health issues.