When you're selling something through a provider, like Craig's List or newspapers, the only thing that may limit your choices is the provider. They may refuse your post if it's against their rules or the law. But luckily they usually don't limit or enforce certain payment choices.
These private business providers have the right to do so if they want. You don't need to be their customer. They may state their terms for using the service and even refuse service (before any payment is made).
The fun part is that you may do so as well. Just remember to state your terms in your post so the prospective buyers are aware of them. I've found it best to put payment and delivery terms in separate lines so that they are easily noticeable, for example:
Nice victorian handbasket with gold embroidery, only used once. Signed by the original author. Comes with a certificate of authenticity.
No delivery, only cash payments.