How can I motivate my troop to take initiative in a program he leads that he doesn't seem interested in?

If he wants to give the minimum, then give him the minimum. If it's not his thing put him on something else. If you continue to get minimum effort from him, Clearly that is the type of person he is, so just give him the minimum (evals, responsible, respect) the problems not you, it's a minimum standard environment the services are starting to embace. I showed up in uniform so medals and promotions for everyone. It's this nonsense that has become a cancer in our society. "But Sgt, I made a 180 on my APFT, that is passing, why can't I get promoted"

You cannot motivate someone else by yourself. Internal motivation is the most effective. You can, however, create an environment that will get better results. Start off by listening to the individual to understand what he is interested in. Understanding this is the starting point for figuring out where to go next. To further understand, avoid closed ended questions which would require nothing more than a yes or no. Open ended questions allow him to expound sufficiently to understand more deeply where he is coming from. Determine how his goals match up with and would benefit by this program. Once that is understood, buy in is much easier. Oftentimes a person is apparently non-enthusiastic because he doesn't know where to start. Guide him to the starting point rather than simply telling him how to begin. If it is his idea, he will be much more invested in the program's success and work harder to assure it. In the early stages, his lack of confidence requires more support. Offer to help him in any way you can. Make sure you continue to show interest in the program and how he is doing with it. Your ongoing interest in the project/program reinforces its importance and his value in presenting it

Is the person an introvert?

Tell him it's required for promotion. Also he maybe having problems at home or outside of duty. As a Supervisor it's important to know your people.

Give him a different program he'll be interested in. And let's face it, unless the end result of not executing the program is physical or mental harm, death, destruction of property, or fraud, then the program isn't actually that important.