The Reagan administration's tuition tax credit bill has been delayed for a month -- and possibly until next year -- because of lingering doubts about the administration's position on discrimination in private schools.

Supporters of the bill asked last week that a final mark-up session be postponed until after Labor Day when they learned that Sen. Bill Bradley (D-N.J.) intended to introduce a package of amendments to strengthen the bill's anti-discrimination provisions. The amendments would give enforcement authority to the Internal Revenue Service, along with the Justice Department.

The administration caused a furor last January when it reversed a long-held government policy and said the Internal Revenue Service has no authority to deny tax-exempt status to schools that discriminate. The decision came in a Supreme Court case involving two fundamentalist schools, Bob Jones University in South Carolina and Goldsboro Christian Schools in North Carolina.

Sen. Daniel Patrick Moynihan (D-N.Y.) said in Senate Finance Committee sessions that he backs the tuition credit bill but is concerned about its civil rights provisions because of the administration's stand on the Bob Jones/Goldsboro case. Bradley's amendments are meant to still those concerns.

But Bob Baldwin, a lobbyist representing several groups on the religious right, called the Bradley proposals "killer amendments" that would split the coalition backing the measure. He said Christian school groups oppose discrimination, "but are not going to give the IRS or any other government bureaucracy an iron boot that allows them to tramp over schools and parents."

Other proponents, however, say Bradley's amendments will simply force the White House to pick what it wants more: a bill with iron-clad enforcement provisions or peace with its fundamentalist supporters.

Bradley, who supports the tuition tax credit concept, said as much in a news conference Friday. "There is a reluctance on the part of a segment conservative church groups to have IRS oversight and to me that is essential to the legislation."

He said no one in the administration had told him " 'Gee, senator, we're in a bind.' " But he added, "At some point there's going to have to be a choice made [at the White House]. Are there strong anti-discrimination provisions in the bill, with IRS oversight, or are there not? I think the majority of the Finance Committee will support strong provisions."

Administration officials declined to discuss their position. But Robert Smith, executive director of the Council for American Private Education, said his impression was that they would try to find some way to accommodate Bradley's concerns in the bill.

He said that the administration made its task in passing the bill "tremendously more difficult" by its action in the Bob Jones case.

Opponents of the measure, which would give parents of private school children a $500 annual tax credit, say the controversy is poetic justice.

Greg Humphrey, lobbyist for the American Federation of Teachers, said, "It couldn't happen to a nicer bunch of people. The Moral Majority and the Christian fundamentalists have had complete control over the administration on this issue. The fact is this proposal is open to abuse and misuse."

The administration was sensitive to the suspicions raised by its reversal in the Supreme Court case, and officials insist the bill contains adequate anti-discrimination provisions. Before qualifying for use of credits, a school must be tax exempt, and file a statement of non-discrimination. It also would be open to suits filed by the Justice Department upon a finding there is a valid complaint of discrimination. The IRS would have no enforcement role.

In answer to questions asked by Sen. Bob Packwood (R-Ore.), however, administration officials acknowledged that Justice Department suits would be dropped without sanction if a school stopped discriminating, and that new suits would have to be filed every three years, the length of time in the bill for taking away credits.

Bradley's amendments would make it clear that the IRS has concurrent authority with Justice, that complainants could file suit themselves if the attorney general didn't, and that credits would be disallowed until the school proved it had stopped discriminating, not just for three years.

Baldwin said there might be room for compromise if Bradley recognizes the concerns of the church schools he represents. "The Christian schools to a certain extent are paranoid about government bureaucracy. But they have reason to be," he said. "If Bradley wants to give the IRS carte blanche I doubt there's any possibility for resolution."

He said that the effect of the anti-discrimination concerns by Bradley and Moynihan has been to delay the bill at least a month in the Senate and "probably kill the bill for this session."

"While they're concerned about a half-dozen schools that may discriminate, tens of thousands of poor people--many of them black--are being discriminated against because they are unable to choose to educate their kids in non-public schools," Baldwin said.