Sorry for the delayed reply. By definition a perennial will die back in the winter and regrow in the following season. Shrubs and some groundcover type plants may stay green through the year. You might consider an evergreen species of fern if the area is shady or perhaps a groundcover such as liriope. But these would not bloom. For blooms in shade perhaps a dwarf azalea. In sun/part shade a dwarf gardenia would be nice.
The following web site lists a great list of perennials for Alabama:
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