Research on magnetic systems with broken inversion symmetry has been stimulated by the experimental proof of particlelike configurations known as skyrmions, whose nontrivial topological properties make them ideal candidates for spintronic technology. In this class of materials, Dzyaloshinskii-Moriya interactions (DMI) are present, which favor the stabilization of chiral configurations. Recent advances in material engineering have shown that in confined geometries it is possible to stabilize skyrmionic configurations at zero field. Moreover, it has been shown that in systems based on Pd/Fe bilayers on top of Ir(111) surfaces skyrmions can be as small as a few nanometres in diameter. In this work, we present scanning tunneling microscopy measurements of small Pd/Fe and $Pd_{2}$ / Fe islands on Ir(111) that exhibit a variety of different spin textures, which can be reproduced using discrete spin simulations. These configurations include skyrmions and skyrmionlike states with extra spin rotations such as the target state, which have been of interest due to their promising dynamic properties. Furthermore, using simulations we analyze the stability of these skyrmionic textures as a function of island size, applied field and boundary conditions of the system. An understanding of the parameters and conditions affecting the stability of these magnetic structures in confined geometries is crucial for the development of energetically efficient and optimally sized skyrmion-based devices.