American Express credit card transactions

My parents own a restaurant and I'm helping them to convert their cash-only system to a credit card system. My dad seems really set on offering American Express, but unfortunately they're one of the most expensive credit card vendors around. He says that business travelers will be less inclined to eat at his store if they don't offer American Express. Is there any way of getting around their high fee? Does anyone know if American Express offers a special program for small businesses? What other credit card vendors would you suggest offering instead of American Express?