The Supreme Court declined yesterday to hear an appeal by a Montgomery, Ala., businessman sentenced to 10 years in prison for receiving a booklet in the mail showing children engaged in sex acts.

Over dissents by Justices William J. Brennan and Thurgood Marshall, the court declined to disturb the conviction last year of Wallace Merrell Miller, who had ordered the booklet from Europe.

Miller, who testified that he received the material in his post office box and did not show it or sell it to anyone, argued that his constitutional rights to privacy were violated by amendments to a federal law against child pornography.

The 1977 law outlawed receiving books, films or magazines depicting child pornography for commercial purposes. Amendments in 1984 made it a crime, punishable by a fine of as much as $100,000 and 10 years in prison, to receive such materials for private use.

A federal appeals court upheld Miller's conviction, rejecting his argument that a 1969 Supreme Court case protected him.

In that case, Stanley v. Georgia, Marshall had written that, under the First Amendment, the "state has no business in telling a man, sitting alone in his own home, what books he may read or what films he may watch."

The solicitor general urged the justices to uphold the conviction, saying that it "would make no sense to expand" the 1969 case to include child pornography, "since the arguments supporting the complete elimination of that form of obscenity are most compelling."

Miller's attorney, Mercer University School of Law professor John L. Carroll, said that Miller is free on bond. Carroll said the 10-year sentence was mandatory under a law allowing for resentencing pending the outcome of psychiatric evaluations on Miller.

Carroll said that Miller, who runs a carpet business and has no previous criminal record, may be placed on probation.