Hold a Raffle
Holding a raffle is a classic way to raise money, or in this case, encourage people to donate food. First, you do need a prize or two. Prizes can be just about anything that appeals to the group you have in mind. One great choice is to ask volunteers to donate crafts they've made. Crafting is big business, and you may know a few jewelry makers, woodworkers or quilters who would be willing to donate finished pieces for a good cause. If they have small home-based businesses selling their crafts for extra money, they might also appreciate the publicity (not to mention the oohs and aahs). Buy rolls of raffle tickets at your local party store and conduct multiple raffles, one for each finished craft project. Display the crafts where they'll be easy to inspect and admire. Make the cost of a ticket an item of food.
If you get lots of craft donations, a bazaar theme is a nice touch that will pull everything together.