I found it! Perhaps, the answer will help someone.
MMM-TTS need a string as “payload” not an array. So, here is my solution :

    {
        module: "MMM-ModuleScheduler",
        config: {
            notification_schedule: [
                {notification: "MMM-TTS", schedule: "45 6 * * *", payload: "Have a nice day. Courage."},
                {notification: "MMM-TTS", schedule: "0 8 * * *", payload: "Do a barrel roll!"}
            ]
        }
    },

Easy-peasy!