Creeping thyme can make a great and fragrant ground cover. There are multiple species and cultivars that creep and form a dense, weed restricting, mat. You can select the variety you prefer to either keep growth slow, be available for culinary use or flower in vibrant color. Most of these plants will grow in USDA zones 6 to 8.

As a Mediterranean herb, thyme needs full sun conditions. It also needs to have quick-draining, alkaline soil to prosper and the soil beneath or near a pine tree will be on the acid side of the pH range. So sadly it will not work in the particular position that you have in mind. 

Courtesy of NYBG Plant Information Office