Data for Sun's Orbit
A well-known analytical planetary theory is VSOP.  The paper describes six versions, most of which are heliocentric.  One of them (E) is barycentric and has an extra (ninth) body: the Sun.  Hence, for VSOP you have the choice of using the Solar System's barycentre as the origin and computing the position of an extra body, or of computing heliocentric positions of the planets directly.

If you use a different theory, I would expect something similar: a heliocentric version and/or a barycentric version with equations for the Sun.