A small local organization has asked our 501C3 organization to join in the publication of a business directory listing members of both organizations that are small business owners.
Businesses would pay to be listed. Is this a permissible activity for a charity?

This is to raise funds for your charity, corrrect? I see nothing wrong with it. Only concern would be that you have to be careful if you provide receipts for chariable giving, as you must show the value of the service received (the value of being listed in the directory).