Southern Democratic legislators, disgruntled by the 1984 Democratic presidential nominating process, predicted yesterday that a dozen southern states will band together to have a regional "Super Tuesday" presidential primary in the second week of March of 1988.

They said that nine of 16 southern and border state legislatures have introduced bills to change their 1988 primary dates to March 8 in an effort to give the region a stronger role in the choice of presidential nominees, particularly on the Democratic side.

Three southern states -- Florida, Alabama and Georgia -- already have presidential primaries on that date; Oklahoma had its 1984 convention delegate selection caucuses in the second week in March.

At a news conference at the National Press Club, backers of the southern regional primary led by Florida Gov. Bob Graham (D) said the move has bipartisan support because many southerners think that the nominations have been decided by the time their primary dates roll around. They also identified their region with the mainstream of American politics.

"The candidates have to respond to so many special interests on a state-by-state basis that it leaves them bereft of a national agenda," Graham said. "There's not much left for the mainstream."

The 16 states account for about one-third of the presidential delegates of both parties, 1,253 of the 3,933 Democratic convention delegates in 1984 and 719 of the 2,235 delegates to the Republican National Convention.

They said the states most likely to change are Texas, Tennessee, Kentucky, North Carolina, Missouri, Mississippi, Oklahoma, South Carolina, Arkansas and Louisiana. There appears to be little likelihood, however, that Maryland, Virginia and West Virginia will join the movement.

In Kentucky, a regional primary bill has passed the state Senate. Approval of the state House is expected as early as next week.

John Bragg, deputy speaker of the House in Tennessee, predicted that a bill will clear both chambers of the legislature within the next two weeks; Texas and North Carolina may have special legislative sessions this summer during which they are expected to pass regional primary bills.

The southern spokesmen said a regional primary is more feasible in their area than any other because of the South's historic cohesion.

"We've had more cooperation on this than on anything since the Confederacy," said Democratic state Sen. John Traeger of Texas, chairman of the Southern Legislative Conference.

Graham said Republicans are supporting the regional primary idea because they are likely to have a more open nomination fight in 1988 since President Reagan cannot run for a third term and southern Republicans want to be sure they have some say in the choice of their nominee.

"They generally have fewer candidates and more party cohesion than Democrats, but in 1988 they may have a relatively open and uncontrolled process so they have an interest in structure and orderliness," he said.

Asked if white southerners are not concerned that the Rev. Jesse L. Jackson might win a plurality of delegates in the proposed regional primary, Texas' Traeger responded that "the game changes every four years."