The most common annual species that you’ll find, along with some selections of it, is the golden tickseed or plains coreopsis (tinctoria), native as its name indicates to the plains of the Central U.S. but also to much of the East and the South.It has spread throughout many western and southern states where it can be found in disturbed areas, such as ditches along roadsides.
It has small, but many, yellow flowers with red centers in summer on plants one foot or so high. Tips of petals have notches in them
Coreopsis auriculata or Mouse-ear coreopsis
The mouse-ear coreopsis(auriculata) gets its great name from the two sections of the leaves that stick out like mouse ears. The yellow spring flowers appear above the dark, evergreen foliage. As with the annual coreopsis, this and most the perennials reach 1 to 2 feet tall.
Although native to southern states, it is hardy in USDA zones 4 through 9 which means they can tolerate minus 30 to 30 degrees F average annual winter minimum temperature. Check your zone with the USDA Hardiness Zone Interactive Map
Coreopsis 'nana' or Dwarf mouse-ear coreopsis.
Even lower is a dwarf mouse-ear coreopsis (‘Nana’) which, like the species, spreads but not aggressively. It only reaches 6 to 8 inches high. Plant several of these a foot or so apart to fill in and make a nice colorful mass of flowers in spring.
Coreopsis grandiflora or Large-flowered coreopsis.
Another popular perennial coreopsis is the large-flowered coreopsis (that’s what the species name grandiflora means), with quite a few popular selections. It begins flowering in early summer and, with deadheading, should produce more orange to yellow flowers throughout the summer.
It, too, is native to southern states, can reach 1 to 2 feet tall, and is hardy in zones 4 through 9. The only downside with this species is that it is short-lived, needing replacing every couple of years in the South and every 3 to 4 years in the North.
Coreopsis lanceolata or Lanceleaf coreopsis
The perennial lanceleaf coreopsis (lanceolata) is another southern native, but also is found through the Midwest and is naturalized throughout northeastern states.
It is, in many respects, similar to its large-flowered relative, and may hybridize with it. This one, though, may be longer lived and has most of its leaves at the base of plants.