Wilson and Lorina Dallas have made a fresh attempt for asylum after their initial application was rejected - and two appeals were unsuccessful.
The couple, aged 38 and 31 respectively, are receiving support from the Catholic church they attend in the Springburn area of Glasgow.
Fr John McGrath from St Aloysius told Premier: "The whole of the Glasgow community and here in Springburn - people of all faiths and none - are so supportive of the family.
"Everyone wants them here because they feel that the family are already part of the community."
A religious ordinance issues by Islamic leaders in Pakistan called for their deaths after a row erupted at a wedding Lorina attended in late 2017.
During the ceremony, the mother-of-two was asked why she would not convert to Islam.
The pair were subsequently attacked and even held at gunpoint - prompting them to seek refuge abroad.
Fr John McGrath added: "We're trying to mobilise everyone, the media, the parish and local politicians. Our MPs have been very good.
"I think there are green shoots of hope there, that there will be a favourable decision for the family and they'll be allowed to remain here."
Wilson and Lorina have two children; Liam, nine, and six-year-old Candice. They have been living in Sighthill for more than a year.
They plea has attracted support from local MP Paul Sweeney and Springburn MSP Bob Doris.
The Home Office told the Scottish Herald: "The UK has a proud history of granting asylum to those who need our protection.
"Where a decision has been made that a person does not require international protection removal is only enforced when we and the courts conclude it is safe to do so, with a safe route of return."
Last year, Premier reported on another Christian family fighting deportation from the UK to Pakistan over concerns for their safety.
Click here to listen to Premier's Alex Williams speaking with Fr John McGrath:
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