The first small piece of the oil-saving energy program President Carter has promised America's trading partners took its next to last step through Congress yesterday.

By a vote of 92 to 6, the Senate approved a House-Senate conference compromise giving the federal government some power to order conversion of industrial and utility plants from oil and natural gas to coal or other fuel.

The measure still must go through the House, which is expected to wait until as much of Carter's program as can be salvaged can be pulled together into one package.

In another energy action, House completed general debate and today will consider amendments to a bill strongly opposed by the railroads that would clear the way for construction of competing pipelines to carry coal slurry - pulverized coal mixed with water - from mine to market.

Carter has had no luck pushing through Congress the energy plan he sent it 15 months ago as the "moral equivalent of war" but he reportedly was much more successful at the just-ended economic summit in Bonn in persuading that the United States will have a national energy program in place by the end of this year.

The president also has said the price of domestic oil would be raised to worls levels by 1980, but did not say how. It could be done by congressional approval of Carter's proposed tax on domestic crude oil, by presedential imposition of import fees on foreign oil, or by Carter letting oil price controls expire next year rather than extending them to 1981 as the law empowers him to do.

The other nations at Bonn have been impatiently waiting for the United States to adopt an energy policy because their economic interests are heavily involved. If America can reduce its oil imports, which cost $45 billion last year and amount nearly half the national consumption, that should strengthen the dollar abroad and permit other countries to sell more goods here cheaper.

The coal conversion bill approved by the Senate yesterday provides that most new electric utility and industrial plants shall be build to consume something other than oil or natural gas.

In general, existing utilities must stop using oil by 1990. For existing industrial plants, the government would have to show that conversion was technically and financially feasible before it could force a change.

In all cases, exemptions would be granted where there is no realible supply of coal or where the air pollution caused by burning coal would violate environmental laws or court or-fore it could force a change.

In all cases, exemptions would be granted where there is no reliable supply of coal or whre the air pollution caused by burning coal would violate environmental laws or court orders.

The bill also would outlaw decorative outdoor gas lights - from residences after the first of 1982 and from commercial use six month after regulations are issued by the Dapartment of Energy. Gas lights could remain in historical settings and where needed for light.

Opinions on the bill's impact vary considerably.

Sen. Harrison Schmitt (R.N.M.) opposed it as needless regualtion, saying oil and gas prices are pushing industries to convert to coal as fast as they can in their own interest.

Henry M. Jackson (D. Wash.), leading sponsor of Carter's energy package in the Senate, foresaw the coal bill as saving one million barrells of oil a day by 1985. But Dewey Bartlett (R-Okla.), who also opposed it as unnecessary, said that the administration had never claimed savings of more than 500,000 barrels a day from coal conversion and that congressional changes had probably reduced this to 250,000.

Coal conversion was the easiest part of Carter's five-part energy package on which to win conference agreement. Conferees have agreed on but not completed drafting a catchall encouraging utilities to save energy by such actions as charging less for use of electricity at offpeak hours, and a measure removing federal price controls from newly discovered natural gas by 1985.

The most important part of Carter's energy package is a collection of taxes, chiefly a tax on domestic crude oil to force up the price and cut consumption. Carter calls the oil tax the centerpiece of his program. Most observers think it is dead.