Personally, I think the best way to make Kingsley unpopular without the risk of making him act out of character would be to take his efficiency and enhance it. Kingsley doesn't appear to be a people-pleaser like Fudge. If he thought a reform was necessary, he would push it through, even if the public didn't want it. This could be, for example, a change in the tax system. Maybe wealthy wizarding families have to pay more under Kingsley, and they dislike that, and start a sort of propaganda against him.