Coreopsis prefer a soil that is not nearly what the average garden soils should be, and if grown in fairly rich soils can be very attractive to aphids, Four-lined plant bugs, and Aster leafhoppers. Aside from planting Coreopsis in a leaner, meaner soil sharp water sprays to knock these wee buggers off the plants helps and if this does not do a good control job then an insecticidal soap will work.

Thanks for your suggestions.

Yes, my soil is terrible...mostly clay. I try to amend it, but some spots are better than others. I think I'll give the insecticidal soap a try. I assume I can get that at any garden store...? Is it fairly easy to use?

You can make your own Inseecticidal Soap by mixing 1 teaspoon of any real soap (Ivory, Fels Naptha, Dr, Bronners, etc.) in 1 quart of water, but there are at least two brand names of Insecticidal Soaps available in garden shops. The insecticidal soap is only effective wet and has no residual affect, but you should not spray anytime the plant foliage will be exposed to direct suns rays. Early morning or evening is best.

It looks like a disease with only a few bites of missing leaves.

Have you had lots or rain? Or humidity? Or do you water from overhead (sprinklers or by hand)?

If so, any/all of those things can increase leaf disease.

In my experience, these plants are tough. Water at the base of the plant only now and then should be sufficient. And you clay soil will be a benefit here, as it will hold the moisture for a good long time.