Voice Assistants (VAs) offer convenient, hands-free user interfaces that can help companies better serve their customers. However, without graphical interfaces, VAs are limited in the amount of information they can transmit, introducing new challenges regarding the fairness of VA output as perceived by users (e.g., based on opaque outputs). Previous studies have developed general Voice User Interface (VUI) design guidelines to optimize VA-user interactions, but they lack a focus on fairness. We follow a systematic multiphase process in which we first employ 18 semi-structured expert interviews to connect 4 fairness principles with established VUI design guidelines to achieve VUI fairness rules. We then identify concrete VUI design characteristics using a Systematic Literature Review (SLR) to operationalize these rules. Our integrative design framework for fair VUIs not only shows VUI fairness rules but also provides practitioners with the appropriate design characteristics to explicitly influence the fairness of their VAs.