I would check with the Chamber of Commerce first. They should be able to point you in the right direction.
Myrtle Beach SC: Myrtle Beach Hotels, Resorts, Attractions & Vacation Guide
Things die down quite a bit once the kids go back to school, which begins in late August. After Labor Day it's much quieter. Things liven back up a bit between Thanksgiving and New Year's, and then January and February are usually the quietest months. Can-Am Days (Canadian-American) is in March, which is a busy time, then there's Easter and things gear up again heading into Memorial Day and the summer.
You might also check with Broadway at the Beach. I'm not sure who's in charge of hiring bands for their Celebrity Square area, but it'd be worth checking out.
Myrtle Beach shopping, dining, nightlife, entertainment in one place! Broadway at the Beach (http://www.broadwayatthebeach.com - broken link)