How can we persuade a child who doesn’t want to try fruits because their mother is allergic to them, to try them?

I would approach the situation on two fronts:  1) With the mother and 2) with the child.

  1. I would ask the mother if she is allergic to all fruits, or if there are particular ones that she cannot eat; then I would ask if she ever serves fruit to her child.  If not, would she be willing to?  What reaction does she have to which fruits?  Is she fearful that her child might also have the same allergy?  Has she checked with her pediatrician?  I must admit I have never heard of anyone being allergic to ALL fruits.  Apples?  Bananas?  Berries? Melons?
  2. I would simply make the fruit available to the child, just as with all the children, offering them such a delicious snack.  Perhaps have another child offer the fruit to the child.  In the end, never force the issue with the child but try to discuss it with the mother.
Child cutting fruit