Allegiant Air has seat sales and discounts from time to time, but doesn't have any specific promo codes for use as of June 2015. Like most low-cost carriers, the airline runs on pretty tight margins.
That's not to say that you can't find deals and coupons for Allegiant Air flights. Most of the deals associated with the airline as of June 2015 are for services offered by its partners, including hotel chains and car rental companies. Some of the coupons are for specific locations -- mostly in Florida -- or for particular types of holidays, like golf getaways. Companies like Travelocity sometimes offer partner deals on flights, though strictly speaking these aren't promo codes.