models.py

@register_snippet
class Author(models.Model):
    first_name = models.CharField(max_length=128)
    last_name = models.CharField(max_length=128)
    site = models.ForeignKey('wagtailcore.Site', on_delete=models.CASCADE)

    panels = [
        MultiFieldPanel([
            FieldPanel('first_name', classname='col6 first-name'),
            FieldPanel('last_name', classname='col6 last-name'),
        ], classname='author-name'),
    ]

    class Meta:
        unique_together = ["first_name", "last_name"]
        ordering = ['last_name', 'first_name']

    def __str__(self):
        return "{1}, {0}".format(self.first_name, self.last_name)

    @classmethod
    def listing_queryset(cls, request):
        return cls.objects.filter(site=request.site)

wagtailsnippets-views-chooser.py

### Then make the following change (original just calls items = model.objects.all() for all models)

def choose(request, app_label, model_name):
    model = get_snippet_model_from_url_params(app_label, model_name)

    if getattr(model, 'listing_queryset', None) and callable(model.listing_queryset):
        items = model.listing_queryset(request)
    else:
        items = model.objects.all()