Why do you want to kill the fungus?

Fairy Ring mushroom (Marasmius oreades) is quite edible, and is common
in grass and lawns. If you have it, sample it. If you have no bad
reactions, eat more. I do!

Much depends on what you call a "fairy ring". A circular growth pattern
centered around a maple is probably closer to Armillariella mellea or
similar fungus. This fungus can be symbiotic at times with its host
tree (beneficial), and can also turn saprophytic and kill the tree.
Your description of a dead Acer suggests the fungus is merely eating
and decomposing the roots and woody debris still present underground.
Nothing wrong with that. Nature does it all the time. It's called
recycling.

Armillariella mellea is also edible for many people.

The best thing to do is figure out what the fungus is before you try to
kill it. It might be good for the soil, and get rid of that woody
debris before you have to dig it up.

Daniel B. Wheeler
www.oregonwhitetruffles.com