My wife went to JCM in the early 1980s. During one class, her teacher told the music students how to make changes to the music program of a church where they were recently hired as the music minister. He told them that changes must come, but they need to be made slowly.
Because of my ministry experiences, I've known pastors who wanted to change their teachings on eschatology. Some of those men asked my opinion on how to do that without hurting their congregation. I suggested they do the same thing they do every service--just teach what the Bible says. Using a pulpit to communicate biblical truth is a powerful thing. A saint knowing why they believe something is better than them just being told to believe it. Such education is the third part of the Great Commission, which says to "teach all things" (Matt 28:19).
And then there's the power of confession. I worked with a Nazarene preacher many years ago. During that time we had many talks about Bible doctrine. He eventually saw the truth of One God and
Acts 2:38 salvation. He took that to his pulpit and confessed what he now knew to be the truth and how that made what he had before taught to be false. He then taught his congregation where these were in the Bible so they could also see these truths. He did lose some folks, but many of his congregation saw it, converted, and stayed.
I think the key is sincerity. If a congregation knows their church leaders have a real love for the things of God, I believe they are more apt to trust those leaders. After all, Paul did say to follow him as he follows Christ. Then, if those leaders do their jobs and teach the congregation, God and His word can then do the rest.