hmm never seen this before. Cut it open and see what crawls out. Really not worth fussing over. These plants spring up, go to seed, and it's all over. They tend to reseed themselves liberally so you should have plenty more next year.

That's gross Alstair. Whatever it is I'd burn all the affected parts right away.

I wonder if its been attacked by mites. or it could be a gall response. either way I would dispose of them and not plant coreopsis in the same place for a couple of years.

you could send an image to the RHS and ask them if they know what it is. or even the whole plant in a plastic bag.