Robin Ricks · Gardenality Seed · Zone 8A · 10° to 15° F
It's just the petals being eaten. I have 2 Labs so no self-respecting rabbits come in the yard.

Gardenality.com · Gardenality Genius · Zone 8A · 10° to 15° F
It could be several things eating just the petals. Could still be rabbits but also could be one or more of several types of insects:

Japanese Beetles - These bugs eat away at the flowers, leaving only traces of the fibrous veins behind. Japanese beetles can be controlled with liquid Sevin spray but this chemical will also kill butterflies, bees and other beneficial insects. I just pick Japanese beetles off my plants or knock them off the plants into a pail of soapy water. The fish in my garden pond love to eat them:-) Thing is, it's May right now and this would be a little early for these critters to be showing up in regions where they are prevalent.

Slugs - I haven't ever noticed any problems with slugs on coneflowers however it is possible. Look for any trails of sticky residue left behind on plants or on the ground or other surfaces in the area. If you see these trails fill some jar lids with beer and place these near the plants. The slugs are attracted to the beer and will die when they crawl into it.

Earwigs - These insects will occasionally feed on coneflower petals, resulting in flowers that appear wilted and tattered. I doubt this is the culprit because it sounds like whatever is doing the damage to your plants is eating the entire flower. If it is earwigs, to avoid them invading your coneflowers, try to clean the bed of thick mulch, weeds and compost - ultimately destroying the potential for a desirable earwig habitat. To identify whther or not it is earwigs you can place tubes made of newspaper or plastic around the coneflowers. During the morning you might find earwigs in these tubes.

If you suspect it's rabbits or some other animal eating the petals, maybe try spraying the plants with a hot pepper spray or some type of repellent listed for rabbits and other pests. I use a product called Repels All.