The only airline I'm aware that allows you to redeem a certificate or a voucher on their website is Northwest. If anyone knows of any other airline that allows redemption of certificates or vouchers on their website, I would be interested to know.
There are no months that typically have the lowest fares from North Carolina to Florida on Southwest. With the exception of certain holiday weekends, the latter half of December, and mid-March to mid-April, every single date is covered by a fare sale at some point. Southwest typically announces a fare sale every couple of months (sometimes more often than that) that covers the entire period they are selling at that time with purchase required by a specific date, so every period is overlapped by a fare sale. In addition to regularly advertised fare sales, Southwest posts Internet-only fares every week for travel beginning 21 days later, through the end of the time they are then selling travel.
The best way to keep informed is to subscribe to their e-mail notification through their website.