The Christian Institute is asking people to pray for an evangelical fostering agency seeking to operate according to its faith-based ethos.
Cornerstone, England's only evangelical fostering agency, was challenged by Ofsted over its recruitment policy, which requires carers to be Christian and abide by an evangelical understanding of sexual conduct.
Last year, the High Court upheld the right of the agency to recruit evangelical Christian carers but disagreed with the policy on sexual conduct.
Cornerstone is now appealing the latter part of the High Court's verdict in a two-day hearing this week.
Aidan O'Neill QC, representing Cornerstone, argues that the High Court was wrong to declare the sexual conduct policy unlawful discrimination.
He told the Court of Appeal it was "incoherent" to say that the agency could use only evangelical Christian carers, while at the same time stipulating that this precludes requiring heterosexual sexual conduct, the Press Association reports.
"If we do accept that Cornerstone's policy is objectively justified ... that a fostering agency should be allowed to restrict its services to persons holding the same faith, it is not then for the court to tell them what that faith really is and 'if you only understood your own faith better, you would be welcoming gay people as carers'," he said.
He added, "If you accept that the religion and belief requirements are justified and lawful, that is the end of the matter."
The agency is being supported in its case by The Christian Institute.
"That High Court judgment confirms the freedom of Christian organisations to operate in line with their statement of beliefs," said Simon Calvert, Deputy Director of Public Affairs at The Christian Institute.
"But the Court mistakenly ruled that Cornerstone cannot require its carers to abide by its Christian beliefs on sexual conduct. Cornerstone is appealing this aspect of the ruling."