I've got a standard azara microphylla. It has a vanilla scent during winter, but it's more sort of the scent that you walk past and catch a whiff of, rather than be able to smell on the plant itself.

RP1

If you hav'nt already noticed I've been asking alot of questions about a lot of plants on this forum. Im building a wish list for a year round scent garden. There seem to be alot of plants that I would love to include but I can't get them all so Im doing alot of reserch and I hope to pick the best suited for shape form and scent.
I have:
2 Osmanthus Fragrans
1 Michelia Figo
a zillion 4 O'Clocks (and counting)
1 Confederate Jasmine
1 Pandora vine
1 brunfelsia americana
1 Aglaia Odorata
So spring and summer are for the most part covered. Winter and fall are still a mystery. sugestions are welcome
I have looked into:
Elaeagnus Multiflora
Chimonanthus praecox
Azara microphylla Variegata or standard

My azara lives in a pot on my deck with an eastern exposure on a wild green space in the heart of Seattle. After a wonderful healthy & frgrant year, the leaves are turning black and falling off. I have inspected carefully for pests which I fight frequently (& organically) due to green space proliferation. Please inform. I love this azara microphylla variegata!

Heavinsent,
I've also wanted to try the azara.
For winter, definitely try chimonanthus, but also try a winter honeysuckle. Winter honeysuckle blooms for a longer period of time and is fragrant from a distance. Both plants are great. Eleagnus is good during the fall, but most of my summer plants are still blooming in the fall here - fall fragrance isn't really something I have to worry about.
Being in Louisiana, your conditions should be similar to mine, and both winter honeysuckle and winter sweet are both easy, no care plants here in Texas 15 minutes from the Louisiana border.