While guns are off the welcome list at chains including Chipotle Mexican Grill Inc., Starbucks Corp., and Sonic Corp., a small but growing number of independent restaurateurs around the country are rolling out the red carpet.

Eateries like Shiloh Brew & Chew in Maryville, Tenn., are posting signs saying guns are welcome. All Around Pizza and Deli in Virginia Beach, Va., is offering discounts for patrons who show up armed, while The Cajun Experience in Leesburg, Va., hosts "Second Amendment Wednesdays." At Shooters...