The petition published on the CitizenGo website has attracted 7,500 signatures since being launched on Friday 11th November 2016.
A statement endorsed by signatories said: "I find the council's refusal to allow you to adopt foster children in your care very disappointing and wish to express my support for you.
"It seems to be the case that you are being discriminated against because you hold mainstream views about the importance of a child being raised by a man and a woman."
The couple, who haven't been named, were told by social services their comment that children need both a "mummy and daddy" was "concerning".
After the council ruled allowing them to adopt their two foster children could be "detrimental to the long-term needs of the children", the couple - who already have two adopted children - have asked the authority to review its decision.
The Christian Legal Centre has been supporting the couple, who have been providing foster care for the two children since the beginning of the year.
Chief Executive, Andrea Williams, said: "This couple's viewpoint is lawful and mainstream. The expression of a view that a child needs a mother and a father cannot justify a refusal to even consider a married couple's application to adopt. The separation of this couple from the children at this time is unthinkable."