In the three years since President Reagan carried every southern state except his opponent's native Georgia, Republican fortunes have generally gone sour in Dixie--except for his own.

The Democrats picked off one southern governor's mansion in 1981--Virginia--and two more last year--Texas and Arkansas. If former Democratic governor Edwin W. Edwards unseats Republican incumbent Gov. David C. Treen in Louisiana on Oct. 22--and the polls show him in the lead--it would reduce the ranks of GOP southern governors to Lamar Alexander of Tennessee.

Moreover, the region's 1984 U.S. Senate races seem equally ripe for the Democrats. Tennessee, North Carolina and Texas head the party's list of potential take-away states.

But for all of this movement back toward a solid Democratic South, a discordant note emerges from the political talk at a three-day meeting of the Southern Governors' Association here. Almost to a man, the chief executives say they believe Reagan is as strong or stronger in their states now than he was in 1980.

"If the election were held today, he'd be the favorite in most of the southern states he carried in 1980," said Virginia Gov. Charles S. Robb (D), association chairman.

"Against Sen. John Glenn it might be as close in Tennessee as it was in 1980 when Reagan carried the state by just 4,710 votes , but if it's former vice president Walter F. Mondale the margin would be higher," Alexander said.

"Reagan is still personally popular in North Carolina, and if the economy keeps getting stronger, he'll be in better shape," North Carolina Gov. James B. Hunt said.

"He's still strong in Florida," Gov. Robert Graham (D) said.

The only governor here who seems eager to take on the president is the host, Gov. Mark White (D) of Texas.

But instead of attacking the president's economic policies--the Democratic target of 1982--White is focusing his barbs more narrowly.

He criticizes Reagan for failing to assist drought-stricken west Texas ranchers, and likens the administration's modest aid package to south Texas, where the border economy has been ravaged by devaluation of the Mexican peso, to "the emperors of Rome handing out aspirin to the Christians after they've been mauled by the lions."

That sort of oratory is rare among southern Democrats now, however, and for good reason.

A poll of 1,000 southern voters taken at the end of July by Darden Research, an Atlanta polling firm, showed Reagan's approval rating on the handling of the economy had shot up to 54.6 percent from its low of 33.4 percent just six months earlier. The Darden poll also showed Reagan defeating Mondale by 58 to 38 percent and Glenn by 54 to 41 percent in the South.

Back in January, both Democrats were narrowly ahead of the president in the head-to-head matchups. In intraparty sparring in the latest poll, Glenn led Mondale by 50 to 44 percent.

There is disagreement, however, on whether the Democratic hold on southern governorships will make a difference in the presidential race. Pollster Claibourne Darden says that "the day of the positive endorsement making a difference is long gone."

But George Shipley, a Democratic pollster based in Austin, says he believes that aggressively partisan Democratic governors throughout the region can make a difference in the 1984 presidential race.

"The South is the only place the Democratic Party can go to put together an electoral majority," he said. "They need to have a southerner on the national ticket, and they need to work voter registration like crazy."

In Texas, White is planning the most massive registration drive in state history, with an announced goal of 1 million new voters by the fall of 1984, and a more realistic target of 500,000. Up to half the new registrants will be blacks or Hispanics, Shipley predicted.

Throughout the South, potential Democratic presidential candidate Jesse L. Jackson is leading a drive aimed at registering up to 1.5 million of the region's estimated 3.4 million unregistered voting-age blacks.

Some skeptics, like Darden, question whether those goals will be met.