Given a finite abelian group \(G\), and an action of \(G\) on the complex projective line \(\mathbb{P}^1\), let \(\Gamma\) be a stable nonempty subset of \(\mathbb{P}^1\). In this article, the authors classify the set of \(G\)-equivariant vector bundles over \(X = \mathbb{P}^1 \backslash \Gamma\). The main result is that (1) every such \(G\)-vector bundle is a direct sum of \(G\)-line bundles, and (2) a \(G\)-vector bundle over \(X\) is completely determined by the representations of subgroups \(H\) of \(G\) on the fibres of points with stabilizer equal to \(H\). Also, one can say exactly which sets of representations occur. For example, if \(G\) is cyclic and acts nontrivially on \(X\), then if the fixed point set has cardinality \(\leq 1\), then the bundle is always trivial. If the cardinality of the fixed point set is two, then it is trivial if and only if the representations of the fibers of the two fixed points are equal. -- The proof is done by first considering the case of a cyclic group action. If the action is not cyclic, the \(G\) acts on \(\mathbb{P}^1\) like \(\mathbb{Z}_2 \oplus \mathbb{Z}_2\). This case is treated separately.