Saheb Fadaie and Fatemeh Bakhteri face 18 months and twelve months respectively if two Tehran-based judges uphold their sentences - originally passed in September 2018.
It has emerged the pair were asked by the judges - who have both previously been accused of involvement in human rights violations - to renounce their Christian beliefs.
They have been accused of attacking Islam by discussing Christian doctrine in house churches.
Mervyn Thomas, chief executive of the religious freedoms charity Christian Solidarity Worldwide (CSW) said: "The conviction of Mr Fadaie and Ms Bakhteri for asserting Christian doctrine is not only a grave violation of their right to espouse a religious belief of their choosing, but also criminalises the Christian faith, which the Iranian constitution purports to recognise."
Mr Fadaie is already serving a ten year sentence in Evin prison for "acting against national security" by "promoting Zionist Christianity".
Mr Fadaie - along with fellow Church of Iran members Pastor Yousef Nadarkhani, Mohammadreza Omidi and Yasser Mossayebzadeh - were arrested during raids on Christian homes in the city of Rasht in May 2016.
They were each jailed for a decade - sentences upheld by the same two judges - Hassan Babaee and Ahmad Zargar - in May last year.
Babaee and Zargar are due to announce their decision in the appeals of Mr Fadaie and Ms Bakhteri in the coming days.
Mr Thomas from CSW added: "It is deeply concerning that Judges Babee and Zargar are presiding over their appeal, especially in view of the unacceptable demand for them to renounce their faith; the rejection by these judges of a previous appeal involving Mr Fadaie, and the allegations that both judges are implicated in human rights violations.
"We call for the verdict against Mr Fadaie and Ms Bakhteri to be overturned, and urge the Iranian authorities to ensure due process in cases involving religious minorities."
It has been claimed Mr Bakhteri suffered harassment by security agents during the year prior to her sentencing.
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