This steamy old river city, erst-while dominion of Boss Crump, long beset by racial divisions, so laggard economically that it was dubbed "the dark spot on the Sun Belt," is moving into a full-blown revival.

But despite all the signs of rebirth in downtown Memphis, the most exciting development in town may be the program of a Catholic nun, Sister Elizabeth Bonia, to revive a depressed black neighborhood. Through a mix of love, imagination, and sweat-equity housing, Sister Elizabeth is creating a model, not just for neighborhood survival in hard times, but also for how to give poor people a real stake in their own community.

Most Memphians would suggest other developments to prove their city's vitality. Reversing years of senseless downtown demolition, for instance, center-city interests have restored the grand old Peabody Hotel, where the fabled ducks waddle again about the fountain of one of the world's most gracefully designed lobbies.

Five years ago downtown Memphis saw its first recycling of an old commercial structure into apartments, now the Cotton Row historic district, and buildings all about the inner city are being saved from abandonment and occupied by "back-to-the-city" fans and professional offices.

After years of destructive urban renewal and frustrated redevelopment plans, it appears that historic Beale Street, where W.C. Handy gave birth to the blues, will be reborn as an entertainment-restaurant center under the hand of a local developer, John Elkington.

This july, Mud Island, a new $62 million river park linked to center city by a monorail, opens to the public. It features an ingenious five-block-long scale model of the Mississippi's course all the way from Cairo, Ill., to New Orleans, "flowing with 1.2 million gallons of water.

William Morris, mayor of Shelby County (which encompasses Memphis) has tried to bridge the city's racial chasm, help improve downtown design and plan a possible enterprise zone. His moves have compensated for the civic indolence and inattention to improved race relations of city Mayor Wyeth Chandler's administration.

A two-year Memphis Jobs Conference, mixing top local business leaders with neighborhood folk, laid strategy for the city's economic future. The meetings were among the most completely racially integrated I've ever seen -- and that in the city of Martin Luther King's assassination.

Still, the work of Marist Sister Elizabeth Bonia may be Memphis' most fascinating story. Six years ago, fresh from assignment in a Jamacian leper colony, she arrived in the beleaguered inner-city Greenlaw area to confront an atmosphere of deep poverty, crime and discouragement. First, she opened a workshop in a building lent by the Catholic Diocese and invited young people to come in and fix their bikes and lawnmowers. Soon they said, "This place is a mess, let's fix it up."

Thus began the rehabilitation work of CoDe North (Community Development North), the organization Sister Elizabeth set up to garner government and foundation funds and let residents manage their own affairs. In all, 26 houses -- many of them handsome Queen Anne structures dating to the late 1800s -- have been rehabilitated for, and often by low-income tenants.

Sister Elizabeth appealed to everybody and anybody -- from the Memphis Jaycees to local carpenters to the Campaign for Human Development -- for money, volunteer time and materials. Few were able to resist her appeals. Twenty-five neighborhood youths received building-skills training in a cooperative effort with sponsors such as the Memphis AFL-CIO and the Federal CETA (Comprehensive Employment and Training Act). Sixteen are now in the union and soon to become journeymen.

Block clubs were set up to teach every skill from sewing draperies to refinishing furniture. A tool library was opened. CoDe North inaugurated congregate homes for the elderly, provided residents with hearty but inexpensive meals, and "graduated" several back into independent living. A crime-prevention program was turned into skills training -- from high-school equivalency courses, to working with police mobile units, to producing gingerbread trim for restored houses.

A "sweat-equity" housing project gave low-income house buyers -- carefylly screened for stable families -- credit toward the $30,000 to $35,000 price of their houses for each hour of labor they put in on their own or someone else's house. Adults and youth take such pride in the units they've helped restore that the houses are spotlessly maintained. Not a single one has been vandalized.

Now CoDe North is getting into vegetable farming with "intergenerational training and guidance." In one case, an elderly double amputee who has had open-heart surgery supervises teen-agers doing the actual work.

Since she captured a number of federal grants in past years, Sister Elizabeth is not too upset about Reagan's budget cuts. "We became so busy managing federal programs that we didn't have time to develop local resources," she says. So CoDe North recently decided not to apply for a $250,000 grant to work with hard-core juvenile delinquents -- "We thought it would distort our focus."