Well, not really a persuasion phrase but more really something I like to say when the other person is not very found of my idea is:
"Hey what do you think about doing X or Y because K and Z? Does that makes sense?"
It doesn't always makes people accept my idea but it triggers a really honest conversation about the specific topic without the other person feeling like I'm trying to impose an idea.
I'm not sure why it worksI think that the "Does that makes sense?" part makes people think that I'm asking for a advice instead of imposing something.