This paper is concerned with learning transferable contact models for aerial manipulation tasks. We investigate a contact-based approach for enabling unmanned aerial vehicles with cable-suspended passive grippers to compute the attach points on novel payloads for aerial transportation. This is the first time that the problem of autonomously generating contact points for such tasks has been investigated. Our approach builds on the underpinning idea that we can learn a probability density of contacts over objects' surfaces from a single demonstration. We enhance this formulation for encoding aerial transportation tasks while maintaining the one-shot learning paradigm without handcrafting task-dependent features or employing ad-hoc heuristics; the only prior is extrapolated directly from a single demonstration. Our models only rely on the geometrical properties of the payloads computed from a point cloud, and they are robust to partial views. The effectiveness of our approach is evaluated in simulation, in which one or three quadropters are requested to transport previously unseen payloads along a desired trajectory. The contact points and the quadroptors configurations are computed on-the-fly for each test by our apporach and compared with a baseline method, a modified grasp learning algorithm from the literature. Empirical experiments show that the contacts generated by our approach yield a better controllability of the payload for a transportation task. We conclude this paper with a discussion on the strengths and limitations of the presented idea, and our suggested future research directions.