This paper proposes a new method for in vivo and almost real-time identification of biomechanical properties of the human cornea based on non-contact tonometer data. Further goal is to demonstrate the method's functionality based on synthetic data serving as reference. For this purpose, a finite element model of the human eye is constructed to synthetically generate displacement full-fields from different datasets with keratoconus-like degradations. Then, a new approach based on the equilibrium gap method (EGM) combined with a mechanical morphing approach is proposed and used to identify the material parameters from virtual test data sets. In a further step, random absolute noise is added to the virtual test data to investigate the sensitivity of the new approach to noise. As a result, the proposed method shows a relevant accuracy in identifying material parameters based on displacement full fields. At the same time, the method turns out to work almost in real-time (order of a few minutes on a regular work station) and is thus much faster than inverse problems solved by typical forward approaches. On the other hand, the method shows a noticeable sensitivity to rather small noise amplitudes. However, analysis show that the accuracy is sufficient for the identification of diseased tissue properties.