After several heavy frosts, in mid to late fall cut perennial selections back for winter, leaving a couple inches of stems at the base. This helps to protect the “crowns”, often which have basal growth there already, ready for next spring. Avoid cutting back too early in fall to allow birds such as goldfinches to enjoy their seeds. Annual varieties, killed by frost, can be removed and composted (unless they have pests or are diseased).
Dividing & Transplanting: For perennial coreopsis, if they begin looking weak with fewer flowers after three years or so, divide them if needed in spring or early fall. Dig plants, use hand tools to divide into smaller sections, then once replanted keep well-watered until established and growing—several weeks.
Pests/Disease: Coreopsis are a low-maintenance plant, generally with few if any pests or diseases. If you see aphids on stems, just wash off with a forceful stream of water. If plants are starting to rot at the base (crown), chances are they are staying too wet. If this is the case, dig and move plants to a drier site.
Some of those with broader leaves may get the whitish powdery mildew which is more of a cosmetic nuisance than harm to the plant.
If you want to prevent this from spreading, use labeled sprays, several choices being organic, starting when you first see this disease. Unlike most diseases, powdery mildew doesn’t need moisture on leaves to infect them—warm, dry weather suits it just fine.