Is there a simple green slime killer for a goldfish pond?

+1 to Bobs answer, adding plants will help greatly by out competing the algae for nutrients.

A submersible UV sterilizer works wonders, but can be kinda pricey, depending on the size pond you have. You could always make a sweet veggie filter if you have the space for it.

Hth

Copper sulfate and all other poisonous chemicals will also kill or severely harm fish. There are chemicals sold to "eliminate" green water & algae, but they are worthless if not dangerous.

To cut down green water, you need to have plants such as water lilies or some other means of putting shade over the water. Duck weed is an obnoxious tiny leaf that will soon cover a pond, but you won't see green water under it.

There are remedies for algae that are specific for backyard ponds and thoroughly risk-free for use with fish. yet another very previous, yet useful answer to the concern is to apply a roll of barley straw in the pond. because it decomposes it releases organic chemical components which try against algae. Google it for greater information