The nine justices are debating whether opening prayers before public legislative meetings violate the Constitution.

WASHINGTON -- Supreme Court justices appeared confounded Wednesday by how to fashion guidelines for prayer at public meetings at a time of vastly greater diversity of religious belief than earlier in the nation’s history.

The justices have struggled for decades to come up with a coherent set of rules for prayers at public meetings. Past decisions have allowed public bodies, including Congress, state legislatures and city councils, to open their meetings with prayers, but the justices have also ruled that public officials may not take actions that appear to “endorse” a specific set of religious beliefs.

In Wednesday’s oral arguments, the justices considered a dispute over the primarily Christian prayers recited before Town Board meetings in the small city of Greece, near Rochester in upstate New York state. Two residents, Susan Galloway, who is Jewish, and Linda Stephens, an atheist, said that being required to sit through Christian prayers in order to attend the board meetings violated their 1st Amendment rights to religious freedom. Their lawyer asked the court to require the town to use prayers that did not specifically endorse Christian beliefs.

But Justice Samuel Alito noted that the religious beliefs of Americans are no longer limited to traditional faiths such as Catholicism, Protestantism, and Judaism. Now, he said, any framework for public prayer such as the one the two women were asking for, would have to accommodate many other beliefs, such as those of Muslims and Bahais.

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“I don’t see how you can compose a prayer that would be acceptable to all these groups,” he said, repeatedly challenging Douglas Laycock, the lawyer arguing for the two women, to come up with one.

Laycock responded that “I am not a pastor.” He insisted it was possible to find such a prayer, but failed to think of an example.

He asked the court to require the town’s officials to establish guidelines for ministers invited to open their meetings that would require the pastors to use prayers that are nonsectarian and do not require the participation of the public.

Thomas G. Hungar, the lawyer for the town, asserted that Greece’s prayers were in line with those in the country’s historical tradition, something the court had approved in a 1983 decision approving prayers recited before the state Legislature in Nebraska.

While Laycock argued that Greece’s prayers “coerced” people like his clients who had business before the Town Board to participate, Hungar said the audience was free to ignore them. Hungar’s position was backed by a lawyer for the Obama administration.

Justice Anthony Kennedy, who as a swing vote on the court will most likely have to be one of the architects of any new approach, seemed uncomfortable with the positions of both sides.

He said he was “very concerned” that establishing guidelines for prayers as Laycock was advocating would “involve the state very heavily in the censorship and approval of prayers.” But he also expressed concern about Hungar’s historical approach, even though that was the basis for the court ruling in the Nebraska case 30 years ago.

The justices will vote in secret on the case later this week and announce a decision by June.

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Tim.Phelps@latimes.com