Annuals:
Sweet Alyssium/Lobularia maritima - my favorite for containers. Plant with Autumn Crocus like speciosum or sativus(Saffron) for a fall show. Honey scented.
Mirabilis jalapa and M. longifolia/4 oclocks open in late afternoon.
Basil/Ocimum - for spagettii sauce.
Tagetes tenuifolia - citrusy smelling miniature Marigolds in yellow, red and orange.
Petunia old fashoned ones check newer ones for fragrance
Nicotiana sylvestris/Flowering Tobacco have a Petunia-like fragrance
Pansy- Orange and yellow varieties have a honeyed scent. Other colors have little or no scent.
Perilla frutescens Purple or Green Shisho- use for tea. (Purple Coleus to some)
Stock/Matthiola - Petunia-like scent
Cheiranthus cheiri/Wallflower - marshmallow/Hawthorn fragrance
Coreopsis tinctoria/Calliopsis- some people say it is sickly sweet but I like it. There are tall and short kinds.
Dianthus gratianopolitanus/Cheddar Pink - Its evergreen foliage resembles a juniper from a distance.
Salvia coccinea - wild scarlet sage. Most all Salvias/Sages are fragrant in flower or foliage. The Zone 8, S.melissodora is always in flower and has a Kudzu flower scent. Cleveland Sage is another semi-hardy favorite of mine.

Perennials:
Lilium phillipenense- Tall stemmed trumpet clusters in August.
Allium tuberosum and A. odorum - These onions have the same fragrance as the August Lily. A. odoratum flowers in July followed by A. tuberosum in August. Pinch off seed heads or cut later for dry arrangements.
Hosta plantaginea and hybrids/cvs. of it like 'Venus', 'Royal Standard', and 'Sweet Sue'.(These like some mid-day shade) They also share the Lilium phillipenense fragrance.
Pycnanthemem muticum/Mountain Mint- This ironclad has pennyroyal scented foliage dusted with a white coating. For shade or sun.- A favorite of tiny green bees and other pollinators.
Menthol scented P. virginianum and thread leaved P. tenuifolium are also good growing Se. natives.

Bulbs:
For winter/earliest spring in a large pot/tub that can remain undisturbed: plant Winter Aconite/Erianthus,
Crocus chrysanthus cvs. and Hyacinths- Roman Hyacinths are the wild forms. Dutch Hyacinths are the big spike headed ones commonly available. All these are very fragrant on sunny winter/spring days.
Galanthus imperatii like the Ginn's forms have a moderate Hyacinth fragrance as well. Gal.nivalis'Samual Arnott' is
also said to be fragrant on sunny days. Narcissus x jonquilla hybrids all have good fragrance. They flower
early to mid-spring. My favorite is 'Kinglet'. 'Thalia' is widely available.

Vines:
Gelsemium sempervirens has yellow spring flowers with a marshmallowy scent. Evergreen and hardy.
Clematis virginiana/paniculata is a group of similar, vanilla scented, late summer, white flowered
non-evergreen vines. As easy as they come. Clematis stans is hard to find, but has small blue autumnal flowers with a grape candy/Kudzu flower scent.

Herbs:
For touchy/feeley experiences
Catnip/Nepeta cataria soft gray foliage with original or lemon scent. The N.x faassenii has a less pleasant smell.
Calaminthas have a strong almost ether-like smell that attracts cats even more than Catnip
Melissa officinalis 'Aurea'/Golden Lemon Balm- Strong Lemon candy scent.
Scented Geraniums are tropical houseplants usable as annuals. They come in a wide range of scents.
Rosmarinus officinalis/Rosemary - The variety 'Arp' from Texas is much hardier than most at Z6. Beautiful small evergreen bush. There is a larger one named 'Barbeque' with stems just right for Shish-ka-babs.
Thymus herba-baroni/Caraway Thyme is the easiest or toughest Thyme for me. Flat cascading mats of tiny leaves. It is used to flavor a famous beef dish.
Mints come in many new flavors. Spearmint, Pennyroyal, Wintergreen, Pear, Marshmallow, even Hilary's Sweet Mint. Mailorder Richters carries many of these new designer mints.

These are all things that scent the air, more or less, and which would stand a greater chance of surviving in mid-south containers.

With larger containers you can have more options, especially with woody things.

Logees Greenhouse also offers a number of fragrant container plants, mostly indoor for the winter.

Wow. So helpful!