  We determine the Thurston's geometry possesed by any Seifert fibered
conemanifold structure in a Seifert manifold with orbit space $S^2$ and no more
than three exceptional fibres, whose singular set, composed by fibres, has at
most 3 components which can include exceptional or general fibres (the total
number of exceptional and singular fibres is less or equal than three). We also
give the method to obtain the holonomy of that structure. We apply these
results to three families of Seifert manifolds, namely, spherical, Nil
manifolds and manifolds obtained by Dehn surgery in a torus knot $K_{(r,s)}$.
As a consequence we generalize to all torus knots the results obtained in
\cite{LM2015} for the case of the left handle trefoil knot. We associate a plot
to each torus knot for the different geometries, in the spirit of Thurston.
