Landmark's Freedom Baptist Curriculum's Penmanship course suggests teaching cursive penmanship to students three years in a row, in second through fourth grades. However, they offer only this two-semester course. You might spread the course out over more than a single school year.
Landmark's course teaches Palmer method, although it differs from some others in that it stresses ending letters with a tail that reaches up to the mid-line. It seems to me that one of the commonest features of sloppy handwriting is letters that end abruptly, either going straight down to the line or trailing off in a variety of inconsistent styles. Consequently, stressing proper "tails" might well improve the appearance of a child's handwriting. Lessons include instruction and questions regarding penmanship vocabulary. Students trace and copy exercises throughout the text, as well as on weekly quizzes and quarterly tests. Content is clearly Christian and it includes some Bible verses. Print quality in the text is uneven, and the black-and-white style is not as appealing as some of the more-colorful options, but instruction is sound and thorough. Worktext, quizzes, tests, and answer key are included.