I've helped my local shop here start promoting a casual Thursday night event even while they're starting to run FNM, too. We've had good turnout, filling the shop with a mix of about 20 kids, adults, experienced players and new ones, too. Duel decks and precons are common, as are EDH/Commander and an occasional casual draft. The nights aren't really structured with actual rounds and pairings, but some folks prefer that.
Wizards supports stores who do this sort of thing with WPN kits that include posters, DCI cards, and a variety of promo foils. Also, your store can use this as an opportunity to distribute the excess prerelease, launch party, and game day promos they receive.