Yes... I saw it first in Stedman's work (Diagram Techniques in Group Theory, G. E. Stedman, Cambridge University Press, 1990), but it may also exist elsewhere. The basic idea is to combine symmetrization and anti-symmetrization across different sets of strands, roughly in correspondence with the Young tableaux.

The other place to look for more general diagrams for general Lie algebras is Cvitanovic (Group Theory: Birdtracks, Lie's, and Exceptional Groups, Predrag Cvitanović, Princeton University Press, 2008, http://birdtracks.eu/). The text is available online and it is extremely impressive.