The requirement to practice "leadership thru influence" is pretty common. This calls on one to achieve outcomes without direct management controls over budget, staff, etc. Here are some books on this subject of indirect influence (or topics near to it) that I recommend.
"Difficult Conversations: How to Discuss What Matters Most" by Douglas Stone, Bruce Patton and Sheila Heen. This may seem like a more general "difficult conversations" book with no applicability to influencing or negotiation. However, often a necessary prerequisite to influence are the topics covered in this book - getting past arguing, avoiding assumption, understanding what is at stake, speaking with clarity and power, etc. So, perhaps no surprise, this is one of several books derived from work originating from the Harvard Program on Negotiation.
"Influencer: The New Science of Leading Change" by Joseph Grenny and Kerry Patterson. This book is truly adapted from work on "crucial conversations" as it is by those authors. However, this focus is on influence - earning it, using it, etc. Key points are around clarity and measures of objectives, key behaviors to drive results, and how to work with a variety of sources for influence. The final chapter dispels, I think wisely, the notion that good influencers are "born to it" and suggests instead the importance planning, analysis (including introspection) and collaboration.
"Enchantment: The Art of Changing Hearts, Minds and Actions" by Guy Kawasaki. Guy Kawasaki is famous for being there at the earlier years of Apple and having the job title of "Evangelist". This is an interesting book because he breaks "enchantment" down to qualities (like likeability and trustworthiness) but also around actions (preparation, overcoming resistance, etc.). This book admirably covers how to use enchantment responsibly and for good... as opposed to simply, and disreputably, being manipulative.
"Getting to Yes: Negotiating Agreement without Giving In" by Roger Fisher and William Ury. As the title suggest, and the text covers, this book is directly related to negotiation. It is another work derived from Harvard's Program on Negotiation. One of the essential, best, ideas of this book is to be thoughtful, even incremental, about the "yes" one is working toward at a particular moment - e.g., asking someone to say "yes" to discussing a topic before asking them to say "yes" to a particular plan of action on that topic.
"Give and Take: Why Helping Others Drives Our Success" by Adam Grant. Adam Grant is a professor of psychology but on the faculty of the management department at the Wharton School. His work then focuses on the dynamics of human behaviors but in a context of what makes teams successful, what motivates people toward their work, and how to establish effective organizational cultures. This book encourages the reader to consider how successful outcomes are in part the product of stakeholders in close relationships where they are willing (even eager) to give as much or more than they take. This book also makes a point of how outcomes are enormously determined by relationships that have the quality of reciprocity in them.
