The Spelling Book
1690 New England Primer
Konrad Tuchscherer mentions one other possible influence on the creation of the Vai syllabary - the English speller.
"There remains, however, a possible mission influence on the creation of a syllabary which turns, not on individuals, but on one piece of school equipment, the spelling book. ... As even today, the spelling books presented certain words broken up into syllables. We know that Sequoyah, before he invented his syllabary, saw a spelling book. It is ... just possible that ... this gave them the idea of analysing and representing language in syllables." p. 480
Here is where a picture is worth a thousand words. What did a speller look like in the 1830's? This illustration is from a 1690 New England primer. There is evidence that reading was taught in this way up until the 1840's if not later.
"In his lectures and reports beginning in 1841, Mann attacked the alphabetic and syllabic methods of teaching reading as meaningless repetition of "skeleton-shaped ghosts." He pointed out, for example, that l- e- g, does not spell "leg" but "elegy" From Teaching Reading - A History by R. M. Wilson.
Certainly other missionaries were still using a syllabic method to teach reading in 1859. In the Sandwich Islands the missionaries were having students copy "the alphabet, syllabic, and reading lessons of the spelling-book, and the scripture extracts" Polynesian Researches chap.1.
Could the mundane English primer be the inspiration for the Cherokee and Vai syllabaries?