Postcards make a lot of sense for these organizations since they're affordable, they reach a targeted audience and yes, they can convey a concise message through a well-crafted design.
There are plenty of Farmers Market postcard designs out there. The ones I'm drawn to are those that convey the excitement of the outdoor market, show the diversity of fresh produce and local foods, and remind me of the joys of participating in a community outing.
Here are some of the best Farmers Market postcards I've recently come upon:
Carrboro Farmers' Market (design by Courtney Smith):
Postcard Magnets (that's a postcard with a magnet attached)
sampler from magnetbyMail.com:
The classic 'wish you were here' look
Sprouts Farmers Market (Eastlake):
Vintage look for Omaha Farmers Market (design by Nicholas Burroughs):
The wonders of color from the Village of Richfield, Ohio: