Why division is the wrong tool here
Most border perennials are lifted and split every few years and come back stronger. Coneflower is not one of them. It builds a deep central taproot with a woody crown on top, and there is no natural line along which the clump wants to come apart. Splitting it means cutting through that crown and severing the taproot, and a mature plant often takes two full seasons to recover, if it recovers at all.
There is also no reason to do it. Coneflower does not decline in the middle and spread outwards the way a rudbeckia or a hardy geranium does. A well-sited plant simply gets a little wider and better every year. Leave it alone and it will outlast the plants around it.
The one time division is justified is rescue: a plant whose crown is partly rotting, or one that must be moved because a shrub has grown over it. In that case lift the whole plant in early spring just as growth begins, wash the soil off so you can see what you are doing, and cut with a clean knife so that every piece carries both a healthy growing point and a real length of firm root. Anything without both goes in the bin. Replant immediately, at the same depth, and expect no flowers that year.
If you want more plants, take root cuttings or sow seed. Both give you healthy new plants without risking the parent, and both are less work than digging up an established clump.
Root cuttings in the dormant season
Root cuttings are the underused method and they work extremely well on coneflower, because the thick fleshy roots readily make new buds. They are taken while the plant is dormant, which is also when a small amount of root can be removed with the least harm. This is the way to keep a plant you value without gambling the whole clump on a division.
- Expose a few roots in late autumn or winter You do not need to lift the plant. Scrape the soil back on one side of a well-established clump until you can see the thick roots running out from the crown, and choose two or three that are about as thick as a pencil.
- Cut pieces two to three inches long Cut each root off close to the crown and divide it into pieces two to three inches (5 to 8 cm) long. Cut straight across the end that was nearest the crown and at a slant on the far end, so that you can tell which way up each piece goes. Firm the soil back over the parent plant afterwards.
- Insert them the right way up Push each piece vertically into a deep pot of gritty free-draining compost, flat end uppermost, until the top is level with the surface. Cover with a quarter inch (5 mm) of grit. A piece inserted upside down will usually fail.
- Keep them cool and barely moist Stand the pots in a cold frame or an unheated shed. Water once when you insert them and then almost not at all until shoots appear, because a wet dormant root cutting rots. Shoots normally break the surface in spring, six to ten weeks later.
- Pot up once roots are working Wait until the shoot has two or three real leaves and you can see white roots at the drainage holes before potting each cutting into its own pot. Grow it on through its first summer in the pot and plant it out in early autumn or the following spring.
Basal cuttings in spring
In spring, when the new shoots from the crown are three to four inches (8 to 10 cm) tall, you can take basal cuttings. Cut a young shoot off right at its base with a sliver of the firm crown tissue attached, trim off the lower leaves, and insert it into gritty potting mix in a covered propagator out of direct sun.
These root in three to five weeks at around 65F (18C). They are quicker than root cuttings but the strike rate is lower, and every shoot you take is a flowering stem the parent will not produce that year. Take no more than a quarter of the new shoots from any one plant.
Seed, and what it will and will not give you
Seed is the cheapest and easiest route, and for the plain purple-pink species it gives excellent plants that come reasonably true to type. Collect the cones once they are hard, dry and dark, rub them apart over a tray while wearing gloves because the bristles are sharp, and separate the plump seeds from the chaff. Seed needs a cold moist period before it will germinate reliably.
Seed saved from a colored or double plant is a different matter. Those plants are hybrids, they cross freely with whatever else is flowering nearby, and their seedlings revert towards the wild pink with a wide scatter of shapes and shades. This is not a failure; it is simply what hybrids do. If you specifically want the color you bought, seed will not give it to you and neither will division of a struggling plant. Root cuttings from the original plant, taken while it is still healthy, are the only route that keeps it.
Keep notes on what you propagated
Label every batch with the date, the method, and which parent plant by position it came from. Root cuttings and seedlings look identical after their first summer, and the parentage matters enormously two years later when the flowers finally open and you want to know which of your plants is the good one.
Also note the date shoots first appeared on root cuttings and the date seedlings first germinated. Both vary a lot with how cold your winter storage actually was, and after two seasons your own dates will be far more useful to you than any general advice about timing.