Professor Robert Hazell and Dr Bob Morris produced two reports on the topic: Swearing in the New King and Inaugurating a New Reign.
Morris told Premier's News Hour that the oath Prince Charles will have to make when he transitions to King is outdated.
"We're not saying the coronation itself shouldn't be Christian, but there might be ways of responding to a situation where we're no longer just Christians," he said.
"We're certainly no longer just Anglican Christians. A little over half the population is prepared to say it has no religious affiliation at all, and now of course we have the important number of people who belong to non-Christian faiths."
He added that the oath requires Charles to swear to support a Church which is established only in England and not in Scotland, Northern Ireland or Wales.
The report states that the new King could "make promises in tune with a more secular and diverse society and a more decentralised Union state".
Another recommendation is that people of other denominations and faiths would attend the ceremony.
Morris said: "The coronation needs to reflect that greater diversity: it will define not just the monarchy, but the whole nation whom the monarch is to represent".
When Prince Charles becomes King, he will have the title of the supreme governor of the Church of England.
In 2008, he said he prefers the title of Defender of Faith, instead of Defender of the Faith.
Listen to Dr Bob Morris speaking with Premier's Cara Bentley here:
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