Courting Fame by Karen Stabiner (Harper & Row: $16.95; 254 pp.)

The world needs another sports book like it needs another Super Bowl. One quick browse through a bookstore will quickly show that just about everyone who has ever scored a touchdown, made a basket or hit a home run has later been inclined to write about it. The approach is almost always self-serving. Also dull.

Now, along comes Karen Stabiner, a Santa Monica-based writer, who has, in her new book “Courting Fame,” taken a novel approach to the writing of a sports book. The approach is called journalism.

Stabiner’s book is about the trials and tribulations of teen-age girls seeking to make it big in women’s tennis. Her introduction sums it up best: “Women’s tennis is a renegade sport, lacking in guidelines, ripe for exploitation, located at the intersection of a parent’s unfinished emotional business, a child’s fantasies, and a society’s infatuation with celebrities, especially the pretty, young, female variety.”

Stabiner traveled the circuit, witnessed firsthand the agony and ecstasy of young girls not even old enough to spell those words, got into the hearts and souls of the parents, and watched with disgust as adult agents and promoters groveled for the attention and contract of each new Tracy Austin clone to come onto the scene.

The girls, most of them from Southern California’s tennis hotbed and most of them pupils of Tracy Austin’s coach, Robert Lansdorp--skillfully painted by Stabiner as a disciplinarian/psychologist/personal entrepreneur--are normal teen-agers carrying around with them the pressures of the president of General Motors. Their fragile psyches rise and fall with each missed backhand, each unlucky draw. The game they play is so much less a game than a daily struggle to climb to the pot at the end of the rainbow. And all this at age 14, 15, 16--when most teen-age girls are concentrating on what to wear to the prom.

Stabiner’s book is more a study of human nature than of sport. It chronicles the torment of fathers trying to finance international travel for daughters whose only right to such extravagance is that they hit fuzzy yellow balls with great accuracy. It depicts some of the traveling mothers as near-pathetic, doting nursemaids. And it depicts the entire scene, from junior tennis to the pros, in a range between cutthroat and sleazy.

The book is flawed only slightly by some sloppy editing that allowed Stabiner, apparently a non-tennis player, to call rallies “volleys,” to call 12-point tiebreakers “13-point tiebreakers” and to refer to Laver’s Tennis Resort (in Delray Beach, Fla.) as “Rod Laver’s Tennis Resort,” when actually it is owned and operated by a relative of the former Australian star.

Indeed, the best part of “Courting Fame” is that, for all the jabs the author correctly takes at players, coaches, parents and agents, the characters of Debbie Spence, Melissa Gurney, Shawn Foltz and Marianne Werdel, future stars of the international tennis world, are so well constructed that the reader can’t help but have an ongoing interest in them. Stabiner shows their scars, but she also leaves room for some rooting that each may make it to the end of her tennis rainbow.