Three-year-old Niki is a charming little girl with alluring eyes, a serious disease and no permanent home. She is adrift in the District of Columbia's foster care system, waiting for a family willing to adopt her.

Niki is one of nearly 2,200 District children in foster care and one of 214 who need adoptive families. A third of the District's children are now in foster homes in suburban Maryland, including Niki, who is in the care of a Landover family. Another 1,117 Prince George's and Montgomery county children are in foster homes or institutions. In Prince George's, 132 are legally free for adoption, and in Montgomery five are waiting for permanent homes.

All but a handful of the youngsters awaiting adoption are "special needs" children, who are hard to place because of their age, race or health.

In 1977, three months after Niki was born, doctors at Children's Hospital discovered she had cystic fibrosis. For the first 18 months of her life, Niki lived between the Hospital for Sick Children and her mother's home in the District. Unable to cope with her daughter's disease, her mother put Niki up for adoption in 1979, according to social service workers. The baby became a ward of the District's Department of Human Services (DHS).

The Pierce-Warwick Adoption Service, a private D.C. agency that contracts with DHS to find homes for children with special problems, placed Niki with Donna Dougherty, a 24-year-old Baltimore woman whose husband had died of cancer. The adoption never became final.

After 18 months, Dougherty, who also has two young sons, said she began to feel that Niki was so attached to her that she could not leave the house, and that she could not face the prospect of seeing the child die in a few years.

According to Dr. Beryl Rosenstein, who treated Niki in Baltimore, the child has a moderate case of cystic fibrosis, a progressive and eventually fatal disease caused by an enzyme deficiency. The disorder affects the lungs and makes her highly susceptible to infection and colds. Rosenstein said Niki's life expectancy depends on how often she gets sick. The average CF patient lives 18 years, though some now survive into their thirties.

Niki requires physical therapy called "postural drainage" about 20 minutes twice a day. The treatment consists of tapping on the child's back while she is in various positions to dislodge any mucus that has collected in her lungs. She also takes medication to help her digest food and gain weight.

In May, Niki was placed in the Landover home of Willie and Millie Hall, who have raised another CF child. Niki's "doing real well," said Millie Hall, adding that she and her husband are willing to care for Niki as her foster parents as long as possible. But, she says, "I feel we are too old to adopt."

Martha Galdi, a Pierce-Warwick social worker, insists that Niki still needs a permanent home. "She needs parents who can be with her while she's living, to enjoy her, and then most particularly, she needs a mommy and daddy who can be with her when she dies. . . . The danger in foster care is that it's not a permanent commitment."

District social service workers were willing to tell Niki's story and permit use of her photograph in hopes of finding a home for her and other hard-to-place children, but said they could not publish her name. Niki is the name given to her by the Baltimore woman who cared for her.

While handicapped children like Niki are difficult to place, healthy children who are older or black also are difficult to find homes for, according to social workers in the District and in Maryland. The "special needs" children who wait the longest for homes are black, male and more than 6 years old.

Carol Siemens, head of adoptions for the Department of Social Services in Prince George's County, said it is also especially difficult to find foster or adoptive families for adolescents and sibling groups.

Finding homes in Prince George's is particularly hard because many families in that county take foster children from the District, which pays families about $200 per month to cover the care of a child, according to Barbara Hoagwood, who oversees foster care in Prince George's. This compares with an average of $170 per month paid by Prince George's.

In all jurisdictions the subsidies are available to foster parents as well as to many parents who adopt special needs children. Generally, subsidies paid adoptive families are about $50 a month less than those paid foster families in the District and Prince George's. Some extra services and, in some cases, extra money are provided families who adopt children with medical problems. Montgomery County pays a monthly subsidy of $220 to foster and adoptive parents, and $247 a month to families with special needs children. Subsidies and services beyond the basic amounts are decided on a case-by-case basis.

Compared with the difficulties encountered by social service workers in the District and Prince George's, Montgomery workers have been notably successful in finding permanent homes for children. Montgomery adoptions chief Jean Royer said her department gets 30 to 40 calls per month for prospective adopting parents.

Royer said she is pleasantly surprised at the increasing number of people who are willing to adopt children with problems. Recently her agency has placed a 4-year-old with cystic fibrosis, a baby with water on the brain, a child with kidney disease and an Oriental teen-ager.

The Prince George's agency has not had as much success. Carol Siemens said most of the white children in public custody have serious handicaps and social workers have "no luck at all" in finding adoptive homes for them.

Throughout the metropolitan area, workers agree that black children have the hardest time finding homes. For years, adoptions in black families were uncommon because blacks often informally adopted the children of relatives, Siemens said. Also, she added, blacks are often reluctant to deal with public agencies.

These trends are slowly changing. Last year Montgomery County hired part-time social worker Geraldine Robinson to encourage more black families to consider adoption. Robinson said she found that many blacks believed they had to be financially well off to adopt. Robinson has been trying to clear up some of those misconceptions by speaking to church and social groups throughout the county. She is also trying to persuade potential parents to consider older children with problems. "The black families I've been working with tend to be like their white, middle-income counterparts . . . they want healthy babies," she said.

Robinson is meeting with success in black communities. Seven foster parents have adopted their children in the past year, and she has identified 23 black families in the county who are ready to adopt. Four of those families have received children recently and are awaiting final clearance of the adoptions.

In Maryland, when all local attempts to recruit a family for special children fails, agencies often turns to Rudy Miller of WBAL (Channel 11) in Baltimore, Miller's weekly show, "Wednesday's Child," features children in their favorite activities. (District social workers say they are reluctant "advertise" children like Niki, however.)

The show began last October and has featured 29 children. To date, 10 of those children have been adopted, and five others are in the process of meeting potential new families. But as all the social workers point out, there still plenty of children waiting.