We characterize the ideals of the semicrossed product $C_0(X)\times _\phi {\mathbb Z}_+$, associated with suitable sequences of closed subsets of X, with left (resp. right) approximate unit. As a consequence, we obtain a complete characterization of ideals with left (resp. right) approximate unit under the assumptions that X is metrizable and the dynamical system $(X,\phi )$ contains no periodic points.