  In this paper we discuss continuity properties of the Wick-type star product
on the 2-sphere, interpreted as a coadjoint orbit. Star products on coadjoint
orbits in general have been constructed by different techniques. We compare the
constructions of Alekseev-Lachowska and Karabegov and we prove that they agree
in general. In the case of the 2-sphere we establish the continuity of the star
product, thereby allowing for a completion to a Fr\'echet algebra.
