nanoindentation of coatings can be calculated using a spherical indenter. There are some derivations in contact mechanics which can provide a relationship between stress and starin using a spherical indenter. .
At first it is vital to define the nature of the load-displacement data. Is your sample elastic, elastic-plastic, viscoelastic or . . . ? And thereby, it is vital to consider the choice of the suitable contact model for your case. I usually recommend not transforming load-displacement to stress-strain as load-displacement data is more convenient to handle and almost every possible mechanical property can be evaluated out of it. I recommend you go through - http://www.sciencedirect.com/science/article/pii/S0009250907000073 which gives a overall survey of suitable contact models and - http://www.sciencedirect.com/science/article/pii/S0009250914001651 which shows how such data can be used for evaluation for the case of elastic-plastic samples.