The button accordion (button box) is a fascinating and beautiful instrument that can present considerable obstacles to those who wish to learn to play it. Because it is a folk instrument, traditionally, most people learn to play by ear and are already familiar with the tunes they wish to play.
Many others find an experienced player and teacher who will introduce the student to new tunes and provide some sort of fingering diagrams (tablatures) to aid the student in playing the instrument. Typically, this tablature notation provides very little, if any, timing requiring the student be very familiar with the tune in order play it properly. Tablature systems are almost as varied as the instructors themselves.
There is also a notation called Griffschrift, which does well at providing timing, but it requires learning a unique notation system. Sheet music in Griffschrift is not readily available in the United States.
My philosophy has been that as long as one is willing to learn to play the button accordion, one might as well spend the effort to learn to read conventional music notation. This will ultimately reward the button accordion player with a wealth of available music. For this reason, I promote learning the button box using conventional music notation. This web site has been developed to assist the button box player, both beginning as well as advanced, with music written in conventional notation. I also host a 1-week button box camp for this purpose.
I hope this web site is helpful for you.