No, coreopsis are biennials. The seeds will sprout leaves the first year, flowers and reseeds the second year and it's done. Let the flowers go to seed and drop the dried flowerheads where you want them to grow. They don't transplant well either but you may have some success if you transplant when they very small. Hope this helps.

Thanks Bathgate. Could I take the flower heads to dry off in the greenhouse then plant the seed in the spring.

They need to go through stratification (a long cold winter). Let the seeds mature naturally on the plant. When the seed pods are ripe, they will swell up like a grape. Cultivate area you want to grow them. You can just drop them on the ground or slightly bury them and just leave them there all winter. You will have dozens of new plants next spring. You will probably find them popping up here and there regardless. They reseed themselves quite readily.

Hi, Coreopsis is a genus of 80 - 100 species of annuals and perennials, C grandiflora is a clump forming perennial, but is often grown as an annual, the species grows to 18 - 36" but some cultivars are smaller, C 'gold Star' grows to about 12" and is usually grown as an annual.
Sow seeds of annuals in situ, in succession from early spring to early summer, sow perennial seed in a seed bed in mid spring, alternatively sow seed of either in a propagator at 55-61f in mid or late winter, {perennials will flower the first year from seed, or take basal cuttings in spring, or divide perennials in early spring, Derek.

Derek: If you buy a pack of seeds, you can sow them in Spring. If you are taking seed pods from a plant, they must go through cold period (winter stratification). There's a difference.

Bathgate, whether you buy your seed or save your own makes no difference, they don't need any cold stratification, and germinate easily, in my experience, Derek.

Coreopsis seeds need cold stratification and should be sown in late fall to sprout in spring. Plant the seeds about 1/4” deep. If sown in very early spring the seeds should sprout in about 3 weeks.
http://www.midwestgardentips.com/direct_sow_seeds.html