Robert L. Woodson is not your basic sentimentalist. He is, rather, a no-nonsense resident fellow at the conservative think tank called the American Enterprise Institute.

Though he is black, he has taken some hard shots at the civil rights establishment, at the overreliance of blacks on the federal government, at the whole range of policies and attitudes that constitute the conventional wisdom of America's black leadership.

This hard-eyed man was close to tears when I talked to him last week. He had been looking at the issue of public child-care policy--with an emphasis on adoption services--and he had come across the story of "Joey."

The youngster, now in his teens, was born to a black teen-age mother who, shortly after his birth, surrendered him to a city agency for adoption. That was his first institution. By the time he left grade school, he had lived in four others. He quickly became the clich,e we've been hearing so much about: the hard-to-place black child.

What moved Bob Woodson to the brink of tears was not so much that the boy had reached adolescence without being placed with a family but that so many well-motivated professionals in so many well-meaning institutions had made so little real effort to place him.

For instance, Woodson told me, Joey was six and still living in an institution when he was first listed with an adoption exchange. One would have thought his caretakers were at last serious about finding him a home. But listen to Woodson:

"First, a single black federal worker who wanted to adopt Joey was rejected. (He later adopted two children through another agency.) Next a single black woman with an older child--a good role model in the jargon of the field--applied and was rejected. Joey waited.

"White applicants were routinely rejected, regardless of their ability to make a good home for Joey. Matching by race was more important to Joey's caseworkers than his continued institutionalization. At last a black couple-- the husband was a well-known professional athlete--applied. But foot-dragging by the agency forced them to look elsewhere, and they adopted a son from another state.

"Finally, another black couple wanted Joey. But Joey, by now having lived all of his 12 years in institutions, was not ready for a family. Joint family therapy was considered, but the agency psychologist said that Joey was now unadoptable, fit only for 'the ministry, the services, or prison.'"

Already, he has been in trouble with the law.

One episode sums up for Woodson the meaning of "institution." Some years back, someone offered to buy Joey a bicycle. The director of the institution said no: "It's our policy that children here not own anything."

Joey's story may be more poignant than most, but those who have looked at child care say it is not wildly atypical. Couples or individuals who are interested in adopting children often run into barriers erected--always in "the best interest of the child"--by public agencies. A couple may be too old, too fat, or disabled, or of the wrong race or religion. Agencies frequently wait passively for natural parents to relinquish their long-since-abandoned children instead of moving aggressively to clear the children for adoption. Private or grass-roots organizations that could help find homes for many of these children often are not enlisted or even informed as to their availability. Rarely are efforts made to exchange information among agencies--in Woodson's description, the counterpart of the real estate industry's multiple listings.

Do agencies assume a proprietary interest in the children in their charge? Is it possible that some agencies cling to adoptable children to justify their own continued existence?

"I don't think it happens like that," says one man who has studied the problem. "I don't think any agency director says, 'Let's keep these 40 kids so we can keep our staff busy,' or anything like that," says Bob Piasecki of Philadelphia.

"What happens is that once a kid gets into a group home, there often is no real thought of getting him into a family situation again. Institutions don't want to make mistakes by placing children in adoptive situations that turn out badly, so they stick with foster care arrangements over which they retain control."

Whatever the validity of the explanations, the result is that children who need permanent homes and families willing, even eager, to provide that permanence, frequently don't learn about each other. And after several years of institutionalization, many of the children become, as a psychologist described Joey, "unable to live in a family."

That's the truly hideous cost. The less important cost is in mere dollars. Woodson estimates that it cost $100,000, mostly in federal funds, to "keep Joey from being part of a family."