Giving new twists and fresh style to timeless coming-of-age theme; Golden States, by Michael Cunningham. New York: Crown Publishers Inc. 241 pp.

LAST spring I started up a muddy trail in the woods behind my New Hampshire house and met my first coyote. I had read that they had been seen in New Hampshire in recent years; now I knew. We looked at each other for a time, then we retreated.

Encountering a coyote in the woods is one thing. Michael Cunningham opens his first novel with a more unnerving situation in Los Angeles: ''Coyotes were sneaking into the neighborhood like unwanted guests at a party. They lapped water from swimming pools and devoured every cat that had learned to think of dogs as playmates or harmless nuisances.''

This wildlife evidence that nature is out of balance introduces us to the world of 12-year-old David Stark, whose life is suddenly all out of kilter. His best friend, Billy, turns into his enemy when David sees him humiliated, caught while shoplifting. David's 23-year-old half sister, Janet, has returned from San Francisco to the family's tract house; after being rejected by medical schools, she had decided to give up and marry her lawyer lover, Rob, but now she has called the marriage off and fled home, where she is gathering up her courage to try once more to become a doctor. His mother, first widowed, then divorced, a woman David describes as ''peculiar and kind,'' seems ''to be shrinking inside her skin.'' Lizzie, his 10-year-old sister, has intensified her bratty behavior.

Not present but omnipresent is David and Lizzie's father, a brute who once knocked David down the stairs.

David feels that he must be the protector of his mother and sisters, picturing himself ''flying, with Janet in one arm and Mom in the other, while men with weapons closed in on the house below.'' The novel is filled with such images of a man rescuing women: David drawing ''a man catching a woman on a trapeze,'' or imagining himself catching Lizzie as she ''fell through the ceiling like laundry through a chute.''

And when Rob, another protector of women, shows up to claim Janet and eventually succeeds in persuading her to return to San Francisco with him, David sets off to bring her home. This could perhaps be called the obligatory quest in a coming-of-age novel, but young David gives it freshness.

By the time the novel ends, David will be chasing off a coyote.

Cunningham has a magical way with figures of speech - coffee steams ''with a black adult life of its own,'' a purse droops ''like a sack of jelly'' - and he eases them into a 12-year-old's viewpoint with stunning skill. However much one might object to the theme of the protection of women, one cannot help savoring every moment of this novel. Funny, tender, it is a joy to read.