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It looks like it is receiving too much water.

The soil needs to be able to dry out, thoroughly, down to about 2 or 3 inches into the soil between waterings, even in the heat.

From here, a fungicide, and correcting the overwatering will be necessary.

Here are some articles that will help:

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/testing-moisture-in-plants.htm

https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm

https://www.gardeningknowhow.com/ornamental/flowers/coreopsis/growing-coreopsis-flowers.htm

There are several things that could be happening to your plant, but you should go ahead and prune it back, removing any dead leaves. Coreopsis is a perennial and should come back in spring. Some varieties enjoy a severe pruning in late summer and will come back strongly. You may also want to treat the plant with neem oil just in case, but when water sits on the leaves of this plant, it can turn dark.

https://www.gardeningknowhow.com/ornamental/flowers/coreopsis/growing-coreopsis-flowers.htm
https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm

Yes. Cut your dead coreopsis stems down to the ground if you haven't already. New growth will spring up from the roots.

https://www.gardeningknowhow.com/ornamental/flowers/coreopsis/growing-coreopsis-flowers.htm

If you are buying nursery plants, the best thing to do will be to catch them before they bloom for the year and plant them. They will bloom as usual.

If you do not catch it in time, then planting in early autumn will ensure flowering the following year.

Unfortunately, flowering for the Perennial types will be all about timing.

Here is an article that will help to grow the plant:

https://www.gardeningknowhow.com/ornamental/flowers/coreopsis/growing-coreopsis-flowers.htm

Here are some possibilities:
Sneezeweed, Helenium autumnale
Jerusalem Artichoke, Helianthus tuberosus