A House Agriculture subcommittee, brushing aside Reagan administration and consumer objections, approved a new federal dairy support program yesterday aimed at reducing surpluses by setting up a farmer-financed fund that would pay dairy farmers not to produce milk.

The measure, part of the 1985 farm bill, now goes to the House Agriculture Committee, where little change is anticipated. But Rep. Tony Coelho (D-Calif.), subcommittee chairman, said he expects it to be challenged vigorously on the House floor.

Neither the administration nor the consumer and milk-user lobbies slowed the steamroller that Coelho put together with the National Milk Producers Federation, which wrote most of the dairy bill. The bill breezed through the livestock, dairy and poultry subcommittee on a voice vote, accompanied by mooing sounds from a bovine toy on Coelho's desk.

Mountains of surplus cheese, milk and butter and multibillion-dollar federal outlays have made the dairy program a center of farm-policy controversy since 1981 and a major but elusive target for administration budget-cutters.

Various legislative attempts to reduce price support levels to discourage excess production have had only limited success. After the latest program ended April 1, milk output surged and so did government purchases, required by law.

The bill adopted yesterday would keep milk supports near current levels but would require a diversion program, paying farmers not to produce, when federal surplus purchases exceed 7 billion pounds.

Rep. James R. Olin (D-Va.) predicted that the diversion would repeat the regional shortages and imbalances that occurred during the diversion that ended April 1. The panel rejected, on a 14-to-2 vote, an Olin proposal to cut program costs by simply reducing price supports.

Also rejected, on an 11-to-5 vote, was a proposal by Rep. Steven Gunderson (R-Wis.) to remove a provision that would increase prices paid to farmers in the Southeast -- at the expense of Upper Midwest dairymen who now export large amounts to that region.

Gunderson and regional allies argued that higher prices in the Southeast would stimulate production and create new surplus problems. Coelho, though not specific, said the bill would be "adjusted" somewhat when it is considered by the full committee.

In a $200 million bow to cattlemen, the subcommittee passed an amendment by Rep. Robert F. Smith (R-Ore.) requiring the government to buy an additional 200 million pounds of red meat per year to lessen the market impact of thousands of dairy cows being sent to slaughter when a diversion program starts.

That added to costs of the bill, but Coelho said it was still a good deal. "We are reducing the cost of the present program by about $700 million," he said. "The administration wants to go cold turkey to get farmers out of business and we want a transition to help them leave smoothly if they wish. They kill farmers; we kill cows."