"Mio padre non ne offre alcuna."
It is difficult to understand what this means.Is it that he has a special wine which he will not share? In that case "My father does not offer it to anyone' would be good. But since it is 'them' in your translation, perhaps it is a selection of coffees. It still needs an object in English, or an implied object eg 'He does not offer IT to any of them' But the translation does not help me understand the Italian.
The object is actually any: think of this context, "Il nostro albero è carico di mele, ma mio padre non ne offre alcuna" (our tree is full of apples, but my father doesn't offer any [of them]). The "ne" in this case represents "of them", and "any" is what he isn't offering; it doesn't specify who he should have been offering them to, so perhaps "he doesn't share" would be more natural, but then again "non ne offre alcuna" isn't exactly natural in Italian either.