D.C. congressional Del. Walter E. Fauntroy told the D.C. statehood convention yesterday that its hopes of getting statehood for the city through Congress hinge on dissolution of the coalition of southern Democrats and conservative Republicans that controls Capitol Hill.

With rampant unemployment, high interest rates and thousands of small business failures throughout the country, Fauntroy predicted, the conservatives ultimately "will be so discredited by the bankruptcy of their policies" that their "historic coalition . . . is going to fall apart."

Then, he said, they will be voted out or mute their conservatism, creating a more congenial climate for D.C. statehood.

Also, he said, "Our power . . . is based on the efficacy of black voters, primarily in the South,"a reference to increased responsiveness by ultraconservative southern members of Congress to greatly enlarged black voting blocs in much of the Deep South in recent years.

Statehood convention delegates, rushing to complete writing a constitution by a May 29 deadline, must present the document to city voters and Congress for consideration, probably this fall and next year. If ratified by the voters, it must then be approved by a simple majority of the 435 House members and 100 senators.

"Can we fashion an arithmetic to get 218 votes in the House and 51 in the Senate?" Fauntroy asked the convention yesterday.

Yes, he said, but it won't be easy. One key member, Rep. Julian C. Dixon (D-Calif.), chairman of the House District Appropriations subcommittee, has already said he doubts statehood will get through Congress now. And Rep. Lawrence Coughlin (Pa.), the ranking Republican on the Dixon subcommittee, has said he opposes D.C. statehood.

Acknowledging his own lack of enthusiasm for statehood as a way to attain more autonomy for the District, Fauntroy said a strategy must be found to pull together those legislators who already favor one or more of what he described as the five basic elements of "full self-determination"--budget autonomy, automatic federal payment, control of the court system, power to impose a commuter tax and full voting rights in Congress.

"I've found a majority of members of Congress to support each of these five items individually," he said, "but they all oppose some of the others."

The goal, he said, should be to determine how many will compromise or trade votes on other unrelated issues in support of all five items and see if there are enough to approve statehood "outside the 18 House members and four Senate members from Maryland and Virginia." Most of these, he said, are certain to vote against statehood since "their constituents will see the vote as a vote for a commuter tax."

Fauntroy told reporters later he has no list of congressional members who are committed to statehood. After the constitution is written, he said, he plans to meet with a "tight group" of sympathetic members to discuss strategy for the statehood measure. He said the group includes Sens. Charles McC. Mathias Jr. (R-Md.) and Edward M. Kennedy (D-Mass.) and Reps. Don Edwards (D-Calif.) and Peter W. Rodino Jr. (D-N.J.).

Fauntroy reiterated that convention delegates should write a document that is "simple and familiar" and not larded with social policy, bureaucratic detail or unorthodox concepts.

In other action yesterday, a convention committee unveiled proposed boundaries for the new state. The external boundaries would be similar to those of the present District of Columbia but leave a small federal enclave downtown.