TWO CHILDREN of presidents -- Margaret Truman and Elliott Roosevelt -- now are embarked on writing separate mystery series with differing success.

Murder in Georgetown (Arbor House, $16.95) is Margaret Truman's seventh Washington-based mystery. In six previous novels, she left corpses littering the White House, Supreme Court, Smithsonian, FBI, Capitol Hill, and Embassy Row. This time the body turns up in the C&O Canal.

Truman has become a solid professional, writing with more assurance and inventiveness with each succeeding book. She now goes beyond the Washington scene to character and plot.

Elliott Roosevelt's Murder at Hobcaw Barony (St. Martin's, $15.95) is his third period-piece mystery with First Lady Eleanor Roosevelt having her day as an amateur sleuth. Roosevelt offers little more than name-dropping of real-life celebrities from the 1930s and '40s. If there are a few moments of charming reminiscence, these are hardly enough to compensate for a rickety plot, feeble characterization, and pedestrian prose.

In Truman's latest look at Capitol crime, the victim is Valerie Frolich, the rebellious daughter of the senior senator from New Jersey, who has his eye on the White House with the backing of a wealthy real-estate developer and an influential columnist.

Valerie's beaten body is found in the C&O Canal after a festive barge party that had drawn Washington's rich, famous and powerful. Joe Potamos, a Pulitzer prize-winning investigative reporter bumped to the police beat after alienating the powerful columnist, is assigned to write the obligatory feature on the murder victim. When he begins interviewing her fellow journalism students, he learns about Valerie's missing diary. Was the senator's daughter going to expose the clique of right-wing superpatriots who want her father to be their president.

Potamos, a likeable chap, cheeky but not smart-mouthed, is quite believable as a big-city reporter (after all, Truman is married to a former managing editor and one of her sons is also a newspaperman). It does seem highly improbable, however, that a Washington Post reporter would have enough money in his pocket to shell out $150 to a tipster.

But, then, Potamos does take time from his sideline sleuthing to go to the office to write his assigned stories. Reporters in fiction often don't seem to have to turn in stories.

In exposing a web of conspiracy and secret deals, Potamos gets help from a gruff cop and Roseann, a pianist who plays at Washington bars and parties and picks up useful gossip.

When Roseann is kidnapped, Potamos breaks into a Leesburg country house to confront the power dealers. Truman does like hectic, bang-bang climaxes. Her fictional conspiracy may seem a trifle far-fetched. But then there are those stories about Virginia estates turned into armed camps.

Murder at Hobcaw Barony takes First Lady Eleanor Roosevelt to the South Carolina estate of Bernard Baruch. Among the other house guests are Joan Crawford, Humphrey Bogart, Darryl F. Zanuck and Tallulah Bankhead.

The first lady is delighted to have a week to relax, go horseback riding, and meet the movie stars before FDR comes from Washington for a weekend of fishing. It turns into quite a party -- Bogie drinking his "loudmouth" scotch, Tallulah shedding clothes at the bridge table, and Crawford and Zanuck wanting to be alone.

Then a particularly nasty movie producer is killed in an explosion in his room. Crawford, Bogie, Tallulah, and Zanuck all have reason to hate the producer. He is the type to resurrect an early-career stag film to blackmail Crawford into appearing in one of his movies.

The first lady, meddling in her genteel way, sorts out the clues with the help of her Secret Service agent and a southern sheriff. There's little surprise at the murderer's identity because the circle of suspects is narrowed once the real-life Hollywood stars are eliminated. In the end, Mrs. Roosevelt, Baruch and the sheriff tamper with the truth and hoodwink Walter Winchell, who has come down to Baruch's estate to investigate the producer's death for his report to "Mr. and Mrs. North America and all the ships at sea."

Roosevelt uses the scandalous goings on of the movie set to pad his frail mystery. Some of this Hollywood gossip does seem of questionable taste these many years later. Hide and Seek

ONE OF THE nicest things about Anna Lee, the British private investigator whose debut in Dupe brought an Edgar nomination for Liz Cody, is that she is so refreshingly normal.

Most female private eyes, like their male counterparts, are quirky loners who somehow don't have to contend with the irritations and roadblocks of mundane every-day living.

Not Anna. She rushes to check in on time at the London offices of Brierly Security. There is a bossy office manager who favors the male agents and keeps a close eye on Anna's timecard and expense account. Anna runs into officious baggage-room attendants who won't allow her to claim property after-hours and snotty doctors who are sticklers for National Health regulations. And her landlord won't cut the grass.

In Head Case (Scribner's, $13.95), Anna is assigned to trace a missing teen-ager. Thea Hahn is a gifted, lonely 16-year-old, described as a brilliant student by her tutors and as "no trouble at all" by the cousin with whom she was staying while taking classes in London. Thea's parents appear more worried about scandal than their daughter's disappearance.

It is the police, not Anna, who locate Thea. She has been found wandering, confused and disoriented, outside a Woolworth's near Southampton and has been turned over to a hospital for treatment. Anna is dispatched to escort Thea to a private institution. She finds herself wanting to reach out to this traumatized young girl who huddles in the car's back seat and seeks refuge under a bed. What terrible thing happened to bring Thea to this state?

The police have their suspicions that Thea may be linked to the shooting death of an unidentified man in a Southampton hotel. It is Anna who turns up the information needed to indentify the dead man and to piece together what happened to Thea.

Cody writes with style and authority. Her characters and situations ring wonderfully true. Most of all there is Anna herself, resourceful and capable, yet curiously vulnerable, with a sympathy that embraces the victims of life as well as crime. Waitin' on the Levee

SO SMALL a Carnival (Viking, $15.95) offers cause to shake the summer doldrums and rejoice. Here is an irresistible first novel with a distinctive voice. It is a story of murder, past and present, set in New Orleans, marvelously evoked from August afternoon thunderheads over the sweltering levees to the raucous sound of Bourbon Street at night. It is a New Orleans seeped in a history of violent politics. Under the surface there still festers the deep-rooted disdain and distrust of the New Orleans patricians for the rednecks of northern Louisiana, who elected Huey Long, the populist governor, and later saw him assassinated at the state Capitol.

So Small a Carnival is the result of the collaboration of John William Corrington, southern novelist-poet, and Joyce H. Corrington, his chemist wife.

Their narrator is Wes Colvin, a crime reporter for the New Orleans Item, who is looking for the big story that will take him to New York or Los Angeles or Washington. Colvin goes to a bar to meet an anonymous phone tipster who has promised an incredible story, ringing off with a cryptic mention of a "deduction box."

Colvin walks in on the scene of a ghastly massacre, machine-gunned bodies sprawled in booths and on the floor. Among the victims are Sandy, Colvin's girlfriend, who tended bar while going to college classes, and the drug-dealing brother of one of the reporter's street buddies.

At first, Colvin blames the massacre on Colombian drug-runners shifting their operations to the Gulf port from Miami. Yet he is puzzled that one of the barroom victims turns out to be August Lemoyne, father of the present district attorney and a former state senator who was a bitter foe of Huey Long in the 1930s. What was Lemoyne doing in the bar? Might he have been Colvin's anonymous caller?

Quite a few people seem determined to discourage Colvin's attempt to gather information for a feature on the state senator's early political career. When the Lemoyne parish priest-family confessor is murdered, the reporter suspects some one had reason to cover up the past.

The Corringtons have a feel for place and history. As the narrator-sleuth, Colvin is just right as an ambitious, hard-nosed reporter, and there is an intriguing case of supporting characters from Colvin's street-wise buddy to Sandy's white-trash ex-husband and a tough black homicide cop named "Rat" Trapp. Memorable scenes linger in the mind -- two young lovers still holding hands after being gunned down in a bar booth.

So Small a Carnival is a classy debut for the Corringtons.

Jean M. White reviews mysteries for Book World on the third Sunday of every month.