The couple, whose daughter recently died shortly after birth, have already aborted twin boys because they want a girl, they told Melbourne's Herald-Sun newspaper.
After having their bid to choose the sex of their next child using IVF rejected by an independent panel, they have now taken their plea to the Victorian Civil and Administrative Tribunal.
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"After what we have been through we are due for a bit of luck," the man told the newspaper. "We want to be given the opportunity to have a girl."
Under state law, sex selection using IVF is banned unless it is done to avoid the risk of the baby's inheriting a genetic abnormality or disease.
The tribunal is due to hear the couple's case in March.
