The earliest work to feature sentence diagrams is normally conceded to be S. W. Clark's Practical Grammar (1847). A decade before Clark, however, Frederick A. P. Barnard, who would go on to become president of Columbia College, and for whom Barnard College was named, wrote a very interesting work that is the earliest significant use of graphical symbols to annotate grammatical analysis that I'm aware of.

I've just written an overview and basic analysis for my (long neglected) Early History of Sentence Diagrams project.