The best way to develop a culture of sponsoring on your team is to believe in sponsoring and team building and demonstrate those behaviors consistently yourself. Additionally, as your Coaches are learning how to sponsor and develop teams of their own, be sure to work with them to:
Do it for them
Demonstrate how to lead a 3 way conversation with a Candidate who is exploring Coaching.
Do it with them
Mentor them through the process by debriefing the conversation so that they understand what transpired and what to do on their own,
Watch them do it
Observe them leading a 3 way conversation with a Candidate who is exploring Coaching. Take time to provide positive and helpful feedback that helps them feel more confident and comfortable as they prepare for their next 3 way conversation.
Watch them teach it - Provide ongoing feedback and mentorship to ensure that what was taught is caught and can be passed along. For more information on developing a sponsoring mindset on your team, check out this video.